Since the pseudo-potential lattice-Boltzmann (LB) model was proposed, it has been suffering from low density ratio, small Reynolds number and flow instabilities, which hamper its application in many science and engineering problems. In this work, we analyze the reasons of flow instabilities in the pseudo-potential LB models, and propose some methods to improve the simulation stability. It is shown that the inter-particle interaction force term and the equations of state (EOS) can result in numerical instability in the particle distribution functions and density. Some straightforward and universal techniques are proposed here in order to achieve larger density ratio, higher Reynolds number and lower temperature as well as suppressing spurious velocity in multiphase flow in the pseudo-potential LB models without additional influences on the equilibrium properties in most cases. These methods contribute to extending the pseudo-potential LB models to realistic multiphase flow further. Finally, we demonstrate the method application for droplet splashing with Re = 15000, We = 120 and density ratio = 4792 at 0.45T(c) successfully. (C) 2018 Elsevier Ltd. All rights reserved.