Simulating turbulence by the standard particle method is difficult due to its unphysical pressure fluctuation. However, the particle method has been improved so as to efficiently suppress such a fluctuation in our previous studies. In this paper, the refined particle method is combined with the sub-particle-scale (SPS) turbulence model. The SPS turbulence model is introduced for the Reynolds stress terms in the filtered Navier-Stokes equation. The standard Smagorinsky model is used in the present study. A spilling breaker is simulated and its turbulent characteristics are analyzed. By comparing with experimental data, a predictive validity of the present simulation is shown.