The research on the triangle packing problem has important theoretic significance, which has broad application prospects in material processing, network resource optimization, and so forth. Generally speaking, the orientation of the triangle should be limited in advance, since the triangle packing problem is NP-hard and has continuous properties. For example, the polygon is not allowed to rotate; then, the approximate solution can be obtained by optimization method. This paper studies the triangle packing problem by a new kind of method. Such concepts as angle region, corner-occupying action, corner-occupying strategy, and edge-conjoining strategy are presented in this paper. In addition, an edge-conjoining and corner-occupying algorithm is designed, which is to obtain an approximate solution. It is demonstrated that the proposed algorithm is highly efficient, and by the time complexity analysis and the analogue experiment result is found.