In this paper the spline subdomain approach is applied to the 2D simulations of the temperature distributions for composites containing a single rectangular particle with an interfacial thermal resistance at the interface between the particle and matrix. The bicubic B-splines are used to construct the trial functions for the approximations of the potential fields of composites. Applying the weighted residual point collocation method inside each subdomain and also on the boundaries between different subdomains, a system of linear algebraic equations is set up to determine the unknowns of the trial functions. The temperature distributions both inside the rectangular particle and along the interfaces under different interfacial contact conditions can be simulated approximately. Numerical results which are compared with the available solutions obtained by FEM method illustrate the accuracy and suitability of the present approach for steady-state conduction. Even in the adjacent areas of corners in the rectangular particle, the simulation results are also satisfactory.