In this paper, we investigate vehicular fog computing system and develop an effective parallel offloading scheme. The service time, that addresses task offloading delay, task decomposition and handover cost, is adopted as the metric of offloading performance. We propose an available resource-aware based parallel offloading scheme, which decides target fog nodes by RSU for computation offloading jointly considering effect of vehicles mobility and time-varying computation capability. Based on Hidden Markov model and Markov chain theories, proposed scheme effectively handles the imperfect system state information for fog nodes selection by jointly achieving mobility awareness and computation perception. Simulation results are presented to corroborate the theoretical analysis and validate the effectiveness of the proposed algorithm.