The almost everywhere pointwise and uniform convergences for the generalized KP-II equation are investigated when the initial data is in anisotropic Sobolev space Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4. Firstly, we show that the solution u(x, y, t) converges pointwisely to the initial data Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4 for a.e. Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4 when Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4, Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4. The proof relies upon the Strichartz estimate and high-low frequency decomposition. Secondly, We prove that Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4, Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4 is a necessary condition for the maximal function estimate of the generalized KP-II equation to hold. Finally, by using the Fourier restriction norm method, we establish the nonlinear smoothing estimate to show the uniform convergence of the generalized KP-II equation in Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4 with Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4 and Hs1,s2(R2)f(x,y)∈Hs1,s2(R2)(x,y)∈R2s1≥14s2≥14s1≥14s2≥14Hs1,s2(R2)s1≥32-α4+ϵ,s2>12α≥4.