In this paper, we consider integer solutions (n, p, x, y, z) for the Diophantine equation n^x + (9p)^y = z^2 where n is positive, p is prime
and x, y, z are non-negative. We show that this equation has no solution if n ≡ 1 (mod 4) and p ≡ 1 (mod 4). Moreover, we find solutions
of the Diophantine equation n^x + (9p)^y = z^2 in some cases.