Two-dimensional (2D) ferromagnetic materials with tunable magnetocrystalline anisotropy (MCA) provide unique opportunities for developing the next-generation data-storage and information devices. Herein we systematically investigate the electronic and magnetic properties of the 1T-MX2 (M = Cr, Mn, Fe, Co; X = As, Sb) monolayers, and identify the stable 2D ferromagnets as well as their MCA energies. Notably, the results demonstrate that the biaxial strain and carrier doping effects have a significant influence on their magnetic behaviors. In addition to the robust FM states, three FM monolayers yield tunable MCA depending on the applied strain type and carrier doping values. The dominant contributions to these complicated modifications in MCA are mainly attributed to the strain or carrier doping induced alterations of specific M-derived 3d states, which in turn lead to the changes of their spin-orbit coupling (SOC) energies. These findings show effective approaches to control 2D magnetism and suggest that these 2D FM materials may be promising candidates to design highly efficient memory devices.