Dozens of missing epochs in the monthly gravity product of the satellite mission Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) mission greatly inhibit the complete analysis and full utilization of the data. Despite previous attempts to handle this problem, a general all-purpose gap-filling solution is still lacking. Here we propose a non-parametric, data-adaptive and easy-to-implement approach - composed of the Singular Spectrum Analysis (SSA) gap-filling technique, cross-validation, and spectral testing for significant components - to produce reasonable gap-filling results in the form of spherical harmonic coefficients (SHCs). We demonstrate that this approach is adept at inferring missing data from long-term and oscillatory changes extracted from available observations. A comparison in the spectral domain reveals that the gap-filling result resembles the product of GRACE missions below spherical harmonic degree 30 very well. As the degree increases above 30, the amplitude per degree of the gap-filling result decreases more rapidly than that of GRACE/GRACE-FO SHCs, showing effective suppression of noise. As a result, our approach can reduce noise in the oceans without sacrificing resolutions on land. The gap filling dataset is stored in the “SSA_filing/" folder. Each file represents a monthly result in the form of spherical harmonics. The data format follows the convention of the site ftp://isdcftp.gfz-potsdam.de/grace/. Low degree corrections (degree-1, C20, C30) have been made. The code to generate the dataset is located in the “code_share/“ folder, with an example for C30. The model-based Greenland mass balance result for data validation (results given in the paper) is provided in the "Greenland_SMB-D.txt” file.