This paper presents numerical simulations of a circular cylinder under the action of current or wave only. The model solves the three-dimensional (3D) Reynolds-averaged Navier-Stokes equations using an explicit projection method. The 3D grid system is made of lots of prisms, which are built from a two-dimensional horizontal triangular grid by adding a number of horizontal layers. A non-linear k-ε model, which can take into account the anisotropy of turbulence is incorporated as a turbulence model. Two test cases including the current flows around and regular waves interact with a circular cylinder are used to demonstrate the capability of the model. The model gives reasonable results in comparison with available experimental data.