The critical behavior and vapor liquid equilibrium of Lennard Jones (L J) fluid were investigated by grand ensemble Monte Carlo simulation. Based on the complete scaling, we used Q parameter method combined with histogram reweighting and finite size scaling theory to estimate critical temperature and density of L J fluid. The results show that Tc* is 1.316 4±0.001 7 and ρc* is 0.316 7±0.000 7, which are consistent with those presented in former reports. We also calculated the vapor liquid phase equilibrium properties and critical asymmetry. For the L J fluid we found |t|1-α term dominated the coexistence curve diameter, while the contribution of |t|2β term was weak.