Microservice based cloud architecture becomes a promising solution to deal with the challenges of large-scale intelligent video applications. However, the current service selection methods usually do not consider both the fine-grained online service capability and the features of video tasks, and this will result in the degradation of the overall efficiency of the service composition. In this paper, we propose a novel Performance-aware Service PAth Selection (PSPAS) approach for the microservice based video cloud computing platform. Firstly, we establish a fine-grained time estimation model which synthetically considers the processing capability of microservice instances, the characteristics of video processing tasks, and the data transfer conditions between microservice instances. Then, based on the proposed performance model, we search and update the optimal microservice path by using the shortest path algorithm. Finally, the experiment evaluation results demonstrate the effectiveness of our method.