The pseudo-potential lattice Boltzmann model is versatile in modelling multiphase flows, since the mesoscopic interaction potential enables it to directly describe the nonideal effect evading the tracking or integrating of phase interface. In this paper, we develop an effective pseudo-potential lattice Boltzmann model to simultaneously realize the thermodynamic consistency, the extremely large density ratio and the adjustable surface tension. Decoupling the mesh space from the momentum space by a scale factor, denser lattice nodes depict the transition region more accurately. The high-precision explicit finite difference method further enhances the calculation accuracy of interaction force. The present model is validated to satisfy thermodynamic even at very low temperature, where the liquid-gas density ratio exceeds 1010. The spurious current can be suppressed to a very low level (<0.0007), despite the density ratio reaching tens of thousands. A modified pressure tension is introduced to tune the surface tension free from the influence of the density ratio. The numerical stability of multiphase simulations is significantly improved, and the droplet splashing is successfully reproduced at Reynolds number 25,000, while the density ratio is more than 10,000.