Micromagnetic simulation is an important tool to study magnetization dynamics in magnetic materials. The underlying model is the Landau-Lifshitz-Gilbert equation, which is solved numerically in general. One of the most popular methods is the Gauss-Seidel projection method developed by Xiao-Ping Wang, Carlos Garcia-Cervera, and Weinan E in 2001. In this talk, we present two improved Gauss-Seidel projection methods with unconditional stability. Compared to the original Gauss-Seidel projection method, which solves heat equations 7 times at each step, saving of these two improved methods are about 2/7 and 4/7, which is verified by both 1D and 3D examples for the same accuracy requirement. Application of both methods to a realistic material is also presented with hysteresis loops and magnetization profiles. We also apply these methods to study the magnetization dynamics in antiferromagnetic and ferrimagnetic materials.