Discrete global grid system (DGGS) is a promising data structure for global geo-referenced data sets based on regular, multi-resolution partitions of polyhedra. The equal-area DGGSs, however, have the important theoretical meaning and applied potential on large-scale remote sensing data processing and management. Besides the equal-area property, we should take the needs of different applications on topologies or geometric properties into consideration. So it is very difficult for us to develop a general and open equal-area DGGS generation algorithm both on theory and on practice. In this paper, we introduce a new general algorithm. First, it codes the vertexes and faces on an unfolded icosahedron. Then, it combines two triangle faces sharing the same edge into a quad and builds coordinates systems to describe the grid generated by different partitions. Lastly, it employs the Snyder equal area projection to project grids of different resolutions from plane to sphere. According to the characters of algorithm, we have designed a software model. By simulating exchange progress of network structure and data, it has strong calculation power. We can get different kinds of triangular, rhombic, and hexagonal DGGSs. The result of experiments proves that our algorithm and software model are flexible enough for complex applications.