A multi-resolution moving particle semi-implicit (MPS) method is applied into two-dimensional (2D) free surface flows based on our in-house particle solver MLParticle-SJTU in the present work. Considering the effect of different size particles, both the influence radiuses of two adjacent particles are replaced by the arithmetic mean of their interaction radiuses. Then the modifications for kernel function of differential operator models are derived, respectively. In order to validate the present multi-resolution MPS method, two cases are carried out. Firstly, a hydrostatic case is performed. The results show that the contour of pressure field by multi-resolution MPS is quite in agreement with that by single resolution MPS. Especially, the multi-resolution MPS can still provide a relative smooth pressure together with the single resolution MPS in the vicinity of the interface between the high resolution and low resolution particles. For a long time simulation, the kinetic energy of particles by multi-resolution MPS can decrease quickly to the same level as that of single resolution MPS. In addition, a 2D dam breaking flow is simulated and the multi-resolution case can run stably during the whole simulation. The pressure by the multi-resolution MPS is in agreement with experimental data together with single resolution MPS. The contour of pressure field by the former is also similar to that by the later. Finally, the simulation by multi-resolution MPS is as accurate as the traditional MPS with fine particles distributed in the whole domain and the corresponding CPU time can be reduced.