Mobile devices have certain restrictions such as processing power and network bandwidth. Edge computing can reduce load and delay by migrating the parts of application processing from mobile devices to edge servers. Edge computing is a method that extends cloud computing to the edge of network. Conventional schemes of face recognition based on edge computing can reduce the amount of network transmission data between the edge servers and the cloud servers by preprocessing data on the edge servers. However, the schemes execute each task on a certain resource, thus application response time may increase according to the conditions of computational resources and network. Hence, a task placement system considering the conditions of computational resources and network is necessary. This paper proposes a task placement system for face recognition applications in edge computing. The proposed system calculates estimated response time of possible task placements based on the task placement decision formula. The formula parameterizes power and CPU utilization of computational resources and delay and bandwidth of network. The task placement that minimizes estimated response time is determined. We implemented a prototype of the proposed task placement system and evaluated its performance through experiment.