You might be interested in my posts on perceptions of race in Roman Egypt and people we would consider black in the Roman Empire. The short answer is that colour-based racism was not present in the ancient world although other types of ethnocentric and bigoted views were common. In many respects Africans occupied a similar role as Celts in the Roman imagination since they too existed on the edge of the Roman world and were perceived as being noble barbarians in many respects. It is also worth keeping in mind that this also applies to Africans we would not consider black today and was by no means based on colour but was determined by cultural background and regional affiliation.

If you wanted to know more about the origins of modern racism you should check out /u/victoryfanfare's excellent run-down on how modern racism emerged and rose to prominence in Europe here, as well as looking at this thread on people of colour in Medieval Europe and its follow up thread, and /u/restricteddata's response to What are some of the more notable (scientific) critiques of scientific racism - especially in the 19th century?.