The problem of anti-biases track-to-track association is addressed. The theoretical analysis is given concerning how the topology structure of the point set formed by multi-target tracks is affected by sensor biases, and the topology difference between two point sets is represented by the non-rigid transformation. A point matching model for anti-biases track-to-track association is established, and a relaxation labeling based non-rigid point matching algorithm is proposed. Performance comparisons are implemented in terms of various typical simulation scenarios, such as different range biases, angle biases, target intensities and detection probabilities. Simulation experiments are conducted to verify the superiority of the proposed approach compared to other competing algorithms.