Abstract. In this paper, using the Mountain Pass Lemma without (PS) con-dition due to Ambrosetti and Rabinowitz, we obtain the existence of the non-trivial solitary waves of Generalized Kadomtsev-Petviashvili equation in multi-dimensional spaces and for superlinear nonlinear term f (u) which satisfies some growth condition. By the Pohozaev type variational identity, we obtain the nonexistence of the nontrivial solitary waves for power function nonlinear case, i.e. f (u) = up where p 2(2n - 1)/(2n - 3).