Aside from the Vikings, I don't think there have been any confirmed expeditions. But you may be interested a story about the Malian ruler Mansa Musa, who made a famous pilgrimage to Mecca in 1324, during which he was said to have given away so much gold that he actually devalued the price. Anyway, Arab historian Ibn Fadl Allah al-Umari visited Cairo a few years after Musa passed through and was told this by an emir who had met with him:

I asked sultan Musa how the kingdom fell to him, and he said: 'We belong to a house which hands on the kingship by inheritance. The king who was my predecessor did not believe that it was impossible to discover the furthest limit of the Atlantic Ocean and wished vehemently to do so. So he equipped 200 ships filled with men and the same number equipped with gold, water, and provisions enough to last them for years, and said to the man deputed to lead them: “Do not return until you reach the end of it or your provisions and water give out.”

They departed and a long time passed before anyone came back. Then one ship returned and we asked the captain what news they brought. He said: “Yes, O Sultan, we travelled for a long time until there appeared in the open sea a river with a powerful current. Mine was the last of those ships. The other ships went on ahead but when they reached that place they did not return and no more was seen of them and we do not know what became of them. As for me, I went about at once and did not enter that river.” But the sultan disbelieved him.

Then that sultan got ready 2,000 ships, 1,000 for himself and the men whom he took with him and 1,000 for water and provisions. He left me to deputize for him and embarked on the Atlantic Ocean with his men. That was the last we saw of him and all those who were with him, and so I became king in my own right.'

This is a third-hand story (from Musa to the emir to al-Umari). On the other hand, al-Umari, who could be quite critical of his sources, evidently considered the emir a reliable witness, so we can't dismiss it out of hand. More cynical historians might note that it was quite convenient for the childless previous Mansa to sail off into the sunset, leaving Musa to take the throne for himself, so the story might have been a way of covering up a coup.

Please note that there is no evidence of West Africans actually reaching the Americas before Columbus. But it’s interesting to note that the idea of an expedition across the Atlantic did exist in the 14th century, even if it was just in the imagination of Musa or the emir.