A parabolic-elliptic attraction-repulsion chemotaxis model is considered. By establishing appropriate entropy inequality, based on a fixed point argument, Lp-estimate technique,the generalized Gagliardo-Nirenberg inequality and Moser's iteration, it is proved that the model admits a unique global solution provided the initial cell mass satisfies the condition that ∥ u0 ∥ L1(Ω) ⩽ 4/XαCNG.