We present simulations of branched polymer dynamics based on a sliplink network model, which also accounts for topological change around branch points, i.e., for branch-point diffusion. It is well-known that, with the exception of stars, branched polymers may show a peculiar rheological behavior due to the exceptionally slow relaxation of the backbone chains bridging branch points. Though Brownian simulations based on sliplinks are powerful tools to study the motion of polymers and to predict rheological properties, none of the existing methods can simulate the relaxation of the bridge chains. The reason for that is lack of a rule for network topology rearrangement around branch points, so that entanglements between bridge chains cannot be renewed. Therefore, we introduce in this paper one possible branch-point mobility rule into our primitive chain network model. For star polymers, diffusion coefficients were calculated and compared with experiments. For both star and H-shaped polymers, diffusion was simulated both with and without the new rule, and the effect on linear viscoelasticity was also determined in one case.