Zhurong rover successfully landed on the southern of Utopia Planet of Mars on 15 May 2021. One laser-induced breakdown spectroscopy (LIBS) system, the main payload of the Mars Surface Composition Detector (MarSCoDe), was installed on the Zhurong rover aimed to measure the elements and their abundance in Martian regolith. Now, there are three sets of LIBS system (ChemCam, SuperCam and MarSCoDe) working on Mars at difference landing sites with diverse geologic features. For Mars exploration, cross-validation is necessary to expand the model compatibility, test data validity, and get more available data of the same type payloads. Spectral transformation approach is the first step and crucial for cross-validation of LIBS analysis model. Herein, a new 4-step spectral transformation approach was proposed to transform the LIBS spectra between three different LIBS systems (i.e., ChemCam, MarSCoDe, SDU-LIBS (recorded by self-built LIBS system)), whose data were partly different in spectral characteristics. Based on this approach, SDU-LIBS and MarSCoDe spectra data were transformed into ChemCam uniform and then the three kinds of LIBS data can have more similar spectral features and share one PLS (partial least squares) model for quantitative analysis. Our approach enables to make up the signal differences between different LIBS systems and gets acceptable quantitative analysis results of SDU-LIBS and MarSCoDe spectra using quantitative PLS model built by ChemCam calibration sample set. This work verified feasibility and availability of our approach for cross validation of different LIBS systems. Based on this method, MarSCoDe data were analyzed and got the preliminary satisfying results although no analysis model of laboratory replica payload was available under the existing conditions.