With recent advances in airborne weapons, air combat tends to occur in the form of beyond-visual-range (BVR) combat and multi-aircraft cooperation. Target assignment is critical in multi-aircraft BVR air combat decision-making. Most previous research on target assignment for multi-aircraft cooperative BVR air combat has focused on centralized algorithms, which can be time-consuming and unreliable. This paper proposes an efficient distributed target assignment algorithm called the multi-target consensus-based auction algorithm (MTCBAA). First, by analyzing the main geometric aspects of BVR air combat, a target assignment model for cooperative BVR air combat was established. Next, based on a consensus-based auction algorithm (CBAA), the MTCBAA was developed to solve the target assignment problem by introducing a cooperative decision-making variable. Although the MTCBAA is based on a greedy mechanism, it can guarantee at least 50% global optimization performance, which was proven through a demonstration of the minimum optimization performance of a centralized target assignment algorithm, since the centralized algorithm is equivalent to the MTCBAA. Finally, experiments were conducted, including an experiment that illustrates the operation of the proposed algorithm, Monte Carlo comparisons with a centralized target assignment method based on the immune algorithm, and deployment experiments on a semi-physical simulation platform. Compared with the heuristic target assignment algorithm, the proposed algorithm significantly improved the target assignment efficiency. The practicality of the proposed algorithm was further verified through a distributed semi-physical simulation experiment.