Micro X-ray fluorescence (µXRF) is an atomic spectroscopy for analyzing micro areas of a sample using Xray beams and mapping elemental distribution on the sample by spectrum acquisition at individual pixel positions. We have examined the potential of rapid and non-destructive µXRF analysis to quantitatively determine the chemical composition of geological samples by correcting standardless fundamental parameters (SFP) quantification data. Based on analysis and comparison of a set of certified international standard silicate glass, linear relationships between μXRF SFP quantification data and certified values of Na2O, MgO, Al2O3, SiO2, K2O, CaO, TiO2, MnO, and FeO were developed, and the corresponding calibration equations were calculated. Further tests on flat or uneven homogeneous glass demonstrated that calibrated results of all major elements were similar with certified values, with improved accuracy of ~10%. Analysis of typical geological materials, including pure minerals, heterogeneous basaltic rock, and micro areas, indicated calibrated results were closer to certified/reference values for most elements. This study reveals that µXRF is a promising technique for rapid, non-destructive, and quantitative investigation of chemical composition of specimens at the microscale level. µXRF measurements and calibration equations developed in this study could be used to rapidly characterize geological materials and non-destructively analyze precious extraterrestrial materials.