4 Every man who prays or prophesies with his head covered dishonors his head. 5 But every woman who prays or prophesies with her head uncovered dishonors her head—it is the same as having her head shaved. 6 For if a woman does not cover her head, she might as well have her hair cut off; but if it is a disgrace for a woman to have her hair cut off or her head shaved, then she should cover her head.
7 A man ought not to cover his head,[a] since he is the image and glory of God; but woman is the glory of man. 8 For man did not come from woman, but woman from man; 9 neither was man created for woman, but woman for man. 10 It is for this reason that a woman ought to have authority over her own[b] head, because of the angels. 11 Nevertheless, in the Lord woman is not independent of man, nor is man independent of woman. 12 For as woman came from man, so also man is born of woman. But everything comes from God.
13 Judge for yourselves: Is it proper for a woman to pray to God with her head uncovered? 14 Does not the very nature of things teach you that if a man has long hair, it is a disgrace to him, 15 but that if a woman has long hair, it is her glory? For long hair is given to her as a covering. 16 If anyone wants to be contentious about this, we have no other practice—nor do the churches of God.
The Bible is clear - there is no Biblical mandate for women to cover their heads! Of course there is nothing wrong with a woman covering her head, but the Bible says that it's up to us to decide. Let your culture be your guide as to what women wear when they pray.
Islam and Christianity A Common Word: The Virgin Mary, Hijab and the Muslim Woman.