Computer use agents (CUAs) have shown strong potential for automating complex digital workflows, yet their training remains constrained by costly live environment interaction and limited high-quality supervision. Existing filtered behavior cloning pipelines suffer from imitation bottlenecks, including distribution shift from the expert demonstration and the absence of negative learning signals. Meanwhile, standard trajectory-level reinforcement learning struggles with sparse rewards, ambiguous credit assignment, and high infrastructure costs for long-horizon GUI interaction. In this work, we propose PRO-CUA, a process-reward optimization framework for training CUAs with iterative step-level reinforcement learning. PRO-CUA decouples on-policy environment interaction from policy optimization: the current policy collects states through live rollouts, generates diverse candidate actions for each state, receives step-level feedback from a process reward model (PRM), and is optimized with group-relative advantages. This design enables dense and flexible credit assignment without relying on golden answers or offline expert trajectories, while reducing distribution shift by training on the agent's own execution states. Experiments on live web benchmarks demonstrate the effectiveness of PRO-CUA and the reliability of PRM-guided step-level training.