In recent years, how to generate policies with generalization abilities has become one of the hot issues in the field of deep reinforcement learning, and many related research achievements have appeared. One representative work among them is generalized value iteration network (GVIN). GVIN is a differential planning network that uses a special graph convolution operator to approximately represent a state-transition matrix, and uses the value iteration (VI) process to perform planning during the learning of structure information in irregular graphs, resulting in policies with generalization abilities. In GVIN, each round of VI involves performing value updates synchronously at all states over the entire state space. Since there is no consideration about how to rationally allocate the planning time according to the importance of states, synchronous updates may degrade the planning performance of network when the state space is large. This work applies the idea of asynchronous update to further study GVIN. By defining the priority of each state and performing asynchronous VI, a planning network is proposed, it is called generalized asynchronous value iteration network (GAVIN). In unknown tasks with irregular graph structure, compared with GVIN, GAVIN has a more efficient and effective planning process. Furthermore, this work improves the reinforcement learning algorithm and the graph convolutional operator in GVIN, and their effectiveness are verified by path planning experiments in irregular graphs and real maps.