The time fractional Klein–Kramers model (TFKKM) is obtained by incorporating the subdiffusive mechanisms into the Klein–Kramers formalism. The TFKKM can efficiently express subdiffusion while an external force field is present in the phase space. The model describes the escape of a particle over a barrier and has a significant role in examining a variety of systems including slow (subdiffusion) dynamics. This paper describes a hybrid algorithm adopting the local radial basis functions based finite difference (LRBF–FD) for the numerical solution of the TFKKM. The time discretization is accomplished via the Grünwald-Letnikov formulation with second-order accuracy and the spatial derivatives are discretized by the LRBF–FD. The LRBF–FD is based on the local support domain that causes to a more sparse matrix and overcomes the ill-conditioning associated with the global collocation. The convergence and stability analysis of the time-discrete algorithm are deduced using the energy method. The feasibility and applicability of the LRBF–FD are demonstrated by using irregular domains. Numerical results are compared with analytical solution and with those obtained by other techniques to verify the accuracy and validity of the LRBF–FD.