A new transient analysis method is proposed for general linear dynamic networks, such as on-chip power grid networks, using hybrid GPU-based multicore platform. The new method, called ETBR-GPU, first performs sampling-like reduction on the original circuit matrices where the frequency domain responses at different frequency points can be calculated in parallel on multicore CPU. After the reduction, the reduced circuit matrices, which are dense but well suitable for GPU's data parallel computing, are simulated on GPU. Such reduction based simulation technique is very amenable for parallelization on the hybrid multicore and GPU platforms, where coarse-grained task-level and fine-grained lightweight-thread level parallelism can be both exploited. The proposed method is very general, since it can analyze any linear networks with complicated structures and macromodels, and it does not assume some structure properties in order to build problem-specific preconditioners, as many iterative solvers do. Experiments show that the new method achieves about one or two orders of magnitude speedup when compared to the general LU-based simulation method on some recently published IBM power grid benchmark circuits.