In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation -△pu = f(x)u~(-α) +λg(x)u~β in R~N, where N≥3, 1＜p＜N, λ＞0, 0＜a ＜1, max(p, 2)＜β + 1＜p* = Np/N-p. We prove that there exists a critical value ∧ such that the problem has at least two solutions if 0＜λ＜Λ; at least one solution if λ =∧; and no solutions if λ＞Λ.