Despite catalyzed by fusion proteins of quite different molecular architectures, intracellular, viral, and cell-to-cell fusions are found to have the essential common features and the nearly same nature of transition states. The similarity inspires us to find a more general catalysis mechanism for membrane fusion that minimally depends on the specific structures of fusion proteins. In this work, we built a minimal model for membrane fusion, and by using dissipative particle dynamics simulations, we propose a mechanism that the pulling force generated by fusion proteins initiates the fusion process and the membrane tension regulates the subsequent fusion stages. The model shows different features compared to previous computer simulation studies: the pulling force catalyzes membrane fusion through lipid head overcrowding in the contacting region, leading to an increase in the head-head repulsion and/or the unfavorable head-tail contacts from opposing membranes, both of which destabilize the contacting leaflets and thus promote membrane fusion or vesicle rupture. Our simulations produce a variety of shapes and intermediates, closely resembling cases seen experimentally. Our work strongly supports the view that the tight pulling mechanism is a conserved feature of fusion protein-mediated fusion and that the membrane tension plays an essential role in fusion.