The integer solution to Diophantine equation is an important branch of the number theory, the problem of integer solution to the Diophantine equation x^2+64=4y^n(x,y∈Z) is discussed by using the methods of algebraic number theory and congruence when n=7,11. and that the Diophantine equation x^2+64=4y^n(n=7,11) has no integer solution is proved.