A new test data compression scheme for circular scan is proposed in this paper. For circular scan, the response of the previous test vector is used as the next test vector's template, and only the conflicting bits between the previous response and the next vector are required to be updated. To reduce the test data volume and test application time, the problem addressed here is minimizing the number of conflicting bits by optimally reordering test vectors. Each vector represents a city, and the number of conflicting bits between two test vectors is regarded as the distance between them. Thus, the problem corresponds to the travelling salesman problem (TSP), which is NP-complete. The genetic algorithm is used to solve this problem. The experimental results show that the proposed scheme could reduce the test data volume efficiently without any additional hardware cost.