Severe core disruptive accidents in sodium-cooled fast reactor and core molten materials and the coolant sodium interaction (Fuel-Coolant Interaction, FCI), are one of the international key and difficult problem on the core safety studies of reactor, especially for FCI process, drastic changes of the mult iphase flow and heat transfer between cold and hot molten fluid interface, and molten material forms, deformation and fragmentation and so on. Based on so many difficulties with large deformation and numerical incontinuous problems in mesh method, a meshless moving particle semi-implicit (MPS) method is introduced in this study. This paper focuses on the simulation of freezing and fragmentation behavior of a single molten Type 304 stainless steel droplet penetrating into sodium pool. An effective viscosity model is introduced to take account of the viscosity change during the phase change. The improved MPS algorithm with surface tension model is adopted to a series of simulation of a single molten stainless steel droplet penetrating into the sodium pool in the range of 1 < V_0 < 5m/s , 1430 < T_<drop> < 1700℃ and 300 T_<na> = 300℃ . The penetrating process is simply clarified in this study. The D_<max> value has a tendency to be smaller with increasing T_i and We_a.