At present, smart manufacturing computing framework has faced many challenges such as the lack of an effective framework of fusing computing historical heritages and resource scheduling strategy to guarantee the low-latency requirement. In this paper, we propose a hybrid computing framework and design an intelligent resource scheduling strategy to fulfill the real-time requirement in smart manufacturing with edge computing support. First, a four-layer computing system in a smart manufacturing environment is provided to support the artificial intelligence task operation with the network perspective. Then, a two-phase algorithm for scheduling the computing resources in the edge layer is designed based on greedy and threshold strategies with latency constraints. Finally, a prototype platform was developed. We conducted experiments on the prototype to evaluate the performance of the proposed framework with a comparison of the traditionally-used methods. The proposed strategies have demonstrated the excellent real-time, satisfaction degree (SD), and energy consumption performance of computing services in smart manufacturing with edge computing.