Summary: When a one-dimensional nonlinear evolution equation could be transformed into a bilinear differential form as \(F(D_tD_x)f\cdot f = 0\), Hirota proposed a condition for the above evolution equation to have arbitrary N-soliton solutions, we call it the 1-dimensional Hirota condition. As far as higher-dimensional nonlinear evolution equations go, a similar condition is established in this paper, also we call it a higher-dimensional Hirota condition, a corresponding judging theory is given. As its applications, a few two-dimensional KdV-type equations possessing arbitrary N-soliton solutions are obtained.