In liquid-propellant chemical propulsion systems, the liquid fuel and oxidizer are atomized by impinging jet atomization, mixed and combustions will occur due to auto-ignition inside a chamber. It is important for a performance prediction to simulate the primary atomization phenomenon; especially, the local mixture ratio can be used as indicator of thrust performance, so it is useful to evaluate it from numerical simulations. In this research, to predict local mixture ratio distribution downstream from an impingement point, we propose a numerical method for considering bi-liquid and the mixture and install it to CIP-LSM which is a two-phase flow simulation solver with level-set and MARS method as an interfacial tracking method. A new parameter, β, which is defined as the volume fraction of one liquid in the mixed liquid within a cell is introduced and the solver calculates the advection of β, inflow and outflow flux of β to a cell. SMART method is used for the interpolating value in a cell. By validating this solver, we conducted a simple experiment and the same simulation. From the result, the solver can predict the penetrating length of a liquid jet correctly and it is confirmed that the solver can simulate the mixing of liquids. Then we apply this solver to the numerical simulation of impinging jet atomization. From the result, the inclination angle of fan after the impingement in the bi-liquid condition reasonably agrees with the theoretical value. Also, it is seen that the mixture of liquids can be simulated in this result. We validate the numerical method by comparing numerical results with the experimental results with local mass flux and mixture ratio distributions.