An important problem that arises in fault diagnosis of analog circuit for fault dictionary technique is the test point selection, which is known to be NP-hard. This paper develops a mathematical optimization model for analog test point selection (ATPS) problem and proposes a novel method to solve it based on quantum-inspired evolutionary algorithm (QEA). The proposed method uses the solution produced by the inclusive algorithm to initialize Q-bit individuals and presents a new fitness function to search the global minimum test point set. In addition, an approach for dynamically determining the magnitude of rotation angle is introduced to accelerate the convergent speed. The efficiency of the proposed algorithm is proven by one practical analog circuit example and a group of statistical experiments. Results show that the proposed algorithm, compared with other methods, finds the global minimum set of test points more efficiently and more accurately.