A smoothed particle hydrodynamics (SPH) method is applied for simulating two-dimensional free-surface problems. The SPH method based on the Lagrangian formulation provides realistic flow motions with violent surface deformation, fragmentation and reunification. In this study, the effect of computational parameters in SPH simulation is explored through two-dimensional dam-breaking and sloshing problem. The parameters to be considered are the speed of sound, the frequency of density re-initialization, the number of particle and smoothing length. Through a series of numerical test. detailed information was obtained about how SPH solution can be more stabilized and improved by adjusting computational parameters. Finally, some numerical simulations for various fluid flow problem were carried out based on the parameters chosen through the sensitivity study.