The Chinese government did encourage rapid population growth because they thought it would be beneficial for their economy and army. After the Century of Humiliation the new communist government wanted to rapidly become powerful and more people meant a greater labor force. It seems like this claim is inspired by some speeches Mao gave in which he said that he "wasn't scared" of a nuclear attack because China had such a huge population they could withstand it. This doesn't necessarily mean that the reason population growth was encouraged was to survive nuclear war. It makes more sense that it was for more particle reasons.

There is a wonderful reply here in Mandarin, and I will attempt to translate the gist of it:

Firstly, it must be considered if there was any population explosion.

In the graph posted with regards to the population growth from 1950 - 1979 in countries with GDP similar to China (within 300 USD - 700 USD), it can be seen that China's population growth (in red) was in fact, one of the slower ones. Pakistan, Vietnam, India and Indonesia were all countries that had more rapid population growth than China. Therefore, China did not really experience a population explosion - it was just that they had that many people to begin with.

Secondly, Mao's policy with regards to populating China was not consistent throughout the entire period of communist rule, and so should not be taken as a single policy of encouraging population growth.

From 1949 - 1953, population growth was encouraged, and policies were implemented to lessen birth control measures (i.e no abortions except for situations that may threaten the mother's life).

From 1954 - 1957, the party has started to reconsider its position. Especially since the Korean war has ended, China's large population was starting to pose some problems. The policies during this period changed to encouraging families to plan before having children, and this included a series of newspaper articles on birth control measures.

From 1958 - 1961, three years of famine has caused a noticeable decrease in the population, therefore birth control measures were halted to replenish the total population.

From 1962 - 1965, birth control measures were once again implemented. A specific percentage of 2% growth rate was mentioned, with policies seeing some effect in the cities, but not much in the countryside.

From 1966 - 1970, the cultural revolution occurrence stopped birth control measures. Although the policies were still in place, the government no longer had time to ensure it was adhered to.

From 1971 - 1978, birth control policies were gradually implemented again. The three main ideals the government pushed were 'late' - for couples to try for children only after the age of 24, 'rare' - for couples to have children that are at least 3 years apart, and 'few' - for couples to have no more than 2 children.

Thus, it can be seen, that the Chinese government encouraged population growth for only a very short period of time. In fact, more effort was spent in trying to control the rate of population growth, and implementing birth control measures.

Thirdly, the policies with regards to population growth did not have much correlation to the number of births during that period of time until after 1970.

The graph clearly shows that government policies had little effect on the erratic number of births in the country (most notably encouraging births during 1957 - 1961 did not stop people from having lesser babies), and it was only after the policies in 1970s (which were specific enough in nature) that the government policy showed as correlation to the number of births.

TL; DR No, the is no truth in the claim from World War Z.

No. It's worth noting that China has had a large base population compared to other countries for a long time relative to Western European ones. In 1910 it had about a quarter of the world's population total. It's actually decreased as a percentage since then.

In fact during the Mao era the Chinese government made efforts to encourage birth control(even if Mao personally wanted more), and the total birthrate per thousand fell from 37 to 20. PDF WARNING.

I'll add that I really, really, would not take anything Max Brooks writes on history as actual. This is a man who thinks that the M-16 platform of today is the same as the early service rifles of Vietnam.