A typical electrolyte contains ions and solvent molecules which are mobile.Between the ions and solvent molecules there are long-range electrostatic interactions.Generally speaking,the statistical mechanics of such kind of systems is hard to analysis.The classical Poisson-Boltzmann equation,which is a mean field approximation,works only for the dilute ionic system.In the past years,we were trying to understand this property numerically and analytically.During this procedure,we have developed two kinds of simulation method.The first one is a GPU-based application for accelerating the typical Monte Carlo simulation.To extract the longrange property of electrolyte exactly,this application uses direct summation for energy evaluation instead of any mathematical approximation.Our application reaches a remarkable 440-fold speedup,compared with the serial implementation on CPU.In this talk,Ill give a brief introduction on this application.The second one is a multi-scale simulation method.This algorithm perform a grand canonical Monte Carlo inside a spherical cavity.All the solvent molecular are treated implicitly and the effect of them are represented by a dielectric permittivity.Interactions between the ions are not only the direct interactions,but also the part due to the reaction of system outside the cavity,which is also implicit treated.For dilute and symmetric electrolyte(Cations and anions have same absolute value of charges and the same size),the continues media can be described by Poisson-Boltzmann equation.In this condition,our algorithm achieves good effect.But for general cases,the Poisson-Boltzmann fails.Therefore we need to find a new approach.Recently,we are exploring some way to get and understand the parameters of the multi-scale simulation by the GPU-based large-scale simulation.In this talk,I will firstly introduce the model of this method from statistical mechanics.We will discuss how to obtain the chemical potential,cavity potential and Greens function of linear response via the large-scale Monte Carlo.And we will show some preliminary results.