The increasing amount of space debris poses a persistent threat to the safety of spacecraft. These non-cooperative targets are generally in a tumbling state, which places stringent requirements on the precision of the end-effector pose for capture tasks. Moreover, there are still difficulties in exploring the orientation state space, making it impractical to track targets with complex tumbling states based on reinforcement learning. To track tumbling targets quickly with high accuracy, we propose Two-Axis Matching Path Tracking (TMPT) algorithm. Our algorithm reduces the complexity of orientation exploration and improves the convergence speed through two-axis matching and the self-guidance module. Furthermore, the training environment has been redesigned by adopting staged tumbling target environment, which expands the range of trackable targets. Comparative simulation results demonstrate the efficiency and robustness of the algorithm.