In Gauss domain,the problem of integer solution of the Diophantine equation x2+(2n)2=y9（x,y,n∈〖WTHZ〗Z〖WTBX〗,1≤n≤7)is discussed by using the methods of algebraic number theory and congruence theory .First of all，finding out the results that have been proven when 1≤n≤7.Then,by discussing the two cases that x is odd and x is even respectively,we proved that the Diophantine equation x2+(2n)2=y9（x,y,n∈〖WTHZ〗Z〖WTBX〗) has no integer solution when n=3,5,6,7.Finally the conclusion is reached that the Diophantine equation x2+(2n)2=y9（x,y,n∈〖WTHZ〗Z〖WTBX〗) has no integer solution when 1≤n≤7.