James was born before 1793, the son of James Burrell but his mother is unknown. The place is not known.
His wife was Margaret Swanston. They were married, but the date and place have not been found. Their seven known children were John (1807-?), Lawrence (1808-?), Agnes (1812-?), James (1813-1872), Betty (1814-?), George (1816-?) and Alexander (1827-?).