To mine the process model including multi-concurrent 2-loops of triangles in incomplete logs, an AlphaMatch algorithm based on extended Alpha algorithm was proposed. Two activities in triangle structure could be correctly matched in 2-loops of triangles by AlphaMatch in the log without repeated activity sequence, thus the process model with multi-concurrent 2-loops of triangles could be mined. Firstly, the activities in 2-loops of triangles were divided into two categories according to the number of activities. Then, a matrix of head and tail position of the activities was constructed to match the two categories and a footprint matrix was constructed to show the relationship between activities. Finally, a large number of experiments were carried out on ProM platform from model correctness, mining efficiency, fitness and precison. Experimental results show that the Petri net model including multi-concurrent 2-loops of triangles can be mined efficiently by the proposed algorithm.