The transmission-line laser model (TLLM) is an equivalent-circuit model which provides stable and explicit matrix routines for the solution of the laser rate equations. The application of TLLM method to the analysis of a vertical-cavity surface-emitting laser (VCSEL) requires certain modifications. The theoretical basis of the model is considered, including space discretization of the inhomogeneous VCSEL cavity so that it yields the synchronization condition. The main attention is paid to the modeling of the carrier diffusion phenomena in VCSEL. As an illustration of the basic capabilities of the resulting spatio-temporal matrix model a transient simulation of diffusive turn-off is provided. Most notably, the degradation of the turn-off transient is observed when the top distributed Bragg reflector (DBR) is extended in the vertical direction.