According to a Sewanee University student project, a brown-eyed man can father a blue-eyed child. This is because the genes for brown eyes are dominant, so the father can possess and pass on the genes for blue eyes despite also having brown-eye genes.
The project further states that each person has four genes that determine eye color, two for each of the paired chromosomes. One of these is the gene for either blue or brown eyes, while the other is the gene for either blue or green eyes. A person need only have one gene for brown eyes on one of the chromosomes to have brown eyes, even if all three of the other genes are for blue eyes.