Coastal and offshore area are extremely dynamic regions. Near-shore wave current field affects the layout and design of hydraulic constructions. This paper focuses on establishing a new two dimensional (2D) Boussinesq model with a meshless method, using the local radial basis function collocation method (LRBFCM). The main concept of the LRBFCM is the interpolation function values which is only associated with the neighbouring nodes in the entire domain. The theoretical formulation has been conducted. In contrast to the fully dense matrices with the global methods, the localized approach results in sparse matrices, which could promote the computation efficiency. In the theory of Boussinesq equations (BEs), different types of BEs are relevant to different horizontal velocities and higher-order terms. The model would be implemented to solve ocean engineering, coastal engineering and harbor engineering related wave motion problems.