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For the monthly spherical harmonic coefficients (SHCs) from GRACE, a method using empirical orthogonal function (EOF) and multi-channel singular spectrum analysis (MSSA) is presented to effectively reduce its dimension and remove its strip noise. The dynamic changing of the SHCs is analyzed, and the corresponding changing model is then constructed. The significant annual term and long term trend have been found in the discrete SHCs, which account for 50.6% and 77.4% (after the annual term has been deducted) of the total variance, respectively. The nonlinear model, which constructed from long term trend and annual term, can perfectly reflect the dynamic changing of the SHCs and its inversion results. And the fitting standard deviation of the equivalent water height on grids over global land areas is between 0.3 cm and 14.0 cm, and the average standard deviation is 1.8 cm. This study can provide valuable implications for the research on the parameter changing characteristics of gravity field and geodynamics.