Orc is a computation orchestration language which is designed to specify computational services, such as distributed communication and data manipulation, in a concise and elegant way. Four concurrency primitives allow programmers to orchestrate site calls to achieve a goal, while managing timeouts, priorities, and failures. To guarantee the correctness of Orc model, effective verification support is desirable. Orc has a highly concurrent semantics which introduces the problem of state-explosion to search-based verification methods like model checking. In this paper, we present a new method, called Compositional Partial Order Reduction (CPOR), which aims to provide greater state-space reduction than classic partial order reduction methods in the context of hierarchical concurrent processes. Evaluation shows that CPOR is more effective in reducing the state space than classic partial order reduction methods.