Class integration test order is one of the most important issues in the field of software integration testing. The different integration test orders have great influence on the testing costs and testing efficiency. In order to reduce the test costs, the traditional studies of generating class-level integration test order focused on reducing the total test stub complexities and the number of test stubs. We apply the thought of “bugs should be found as early as possible” to generate the integration test order, and propose an evaluation scheme “Class-HITS” to measure the importance of software nodes. In the proposed scheme, we firstly consider the software as a network based on the complex network theory, and with the help of proposed scheme, the circles of the network are eliminated. Finally, the integration test order is obtained by reverse sorting the nodes in acyclic links. The simulations have been carried out on open-source software, which prove the efficiency of the class integration test order obtained by the proposed scheme. The new algorithm ensures the important nodes with priority to be tested, the smaller total complexity of the test stubs.