In this paper, we study weighted L p−q minimization model which comprises non-smooth, non-convex and non-Lipschitz quasi-norm L p (0 < p ≤ 1) and L q (1 < q ≤ 2) for recovering sparse signals. Based on the restricted isometry property (RIP) condition, we obtain exact sparse signal recovery result. We also obtain the theoretical bound for the weighted L p−q minimization model when measurements are depraved by the noises.