Neuromorphic computing has been getting attention because of its potential for fast and low-power computation, robustness, and learning capability. Though traditional machine learning applications are main target of neuromorphic computing, its characteristic of parallel and distributed processing with simple spike-based signals is useful for other types of applications such as a shortest path finding problem (SPFP) on a graph. Prior work discussed approaches for mapping SPFP to a spiking neural network (SNN). In this paper, we propose an SNN algorithm for path planning with moving obstacles. In real world situation, there are many moving obstacles (such as other cars for an autonomous driving car and human for a moving robot) around a target agent which tries to optimize its own path to the goal. Finding an effective path in such an environment is not an easy task since behavior of obstacles is sometimes unknown and there must be a huge number of candidate paths to go. Traditional methods for SPFP with a general CPU may not be effective since it should compare candidate paths and select the most suitable one every time step. We consider two agents with SNN which tries to achieve two goals: 'reaching its destination promptly' and 'avoiding moving obstacles properly'. Thanks to SNN properties, the agent can learn and estimate how the obstacles move. We compare the proposal approaches with an existing method on a 2D grid graph and the result shows that the proposal agents can select proper paths depending on obstacles' movement.