The Diophantine equation is an important branch of number theory research, not only itself development is active but also it has important application in discrete mathematics, as a result, it plays an important role in solving real problems. Many scholars at home and abroad extensively and deeply study it for many years. By the elementary methods such as pell equation, recurrent sequence, congruence expression, and square residue, the solution to the Diophantine equation x3±64=Dy2 is discussed when D=73, and this paper proves that the Diophantine equation x3±64=73y2 only has integer solution (x,y)=(4,0).