The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. Recently, Mizumachi proved nonlinear stability of 1-line solitons for exponentially localized perturbations. In this paper, we prove stability of 1-line solitons for perturbations in (1 + x 2)−1/2−0 H 1(ℝ2) and perturbations in H 1(ℝ2) ∩ ∂xL 2(ℝ2).