These datasets provide global (excluding Antarctica) reconstructions of the GRACE-like terrestrial water storage anomalies (TWSA) from April 2002 to July 2021 with a spatial resolution of 1 degree. These reconstructed TWSAs were generated by a two-step linear model. The driving data include the ERA5-Land model-extracted precipitation and air temperature data, as well as the Noah model-simulated TWSA. The training period is from April 2002 to April 2013, and the testing period is from May 2013 to July 2021. ‘REC-JPL-M’ means the reconstructed TWSA based on the JPL mascon solution; ‘REC-JPL-SH’ means the reconstructed TWSA based on the JPL spherical harmonic solution.