A full rate-dependent cohesive law is implemented in the distinct lattice spring method (DLSM) to investigate the dynamic fracturing behavior of brittle materials. Both the spring ultimate deformation and spring strength are dependent on the spring deformation rate. From the simulation results, it is found that the dynamic crack propagation velocity can be well predicted by the DLSM through the implemented full rate-dependent cohesive law. Furthermore, a numerical investigation on dynamic branching is also conducted by using the DLSM code.