The high-resolution rovibronic line lists of the MgH+ molecular cation are presented in our work. The potential energy curves are calculated by the method of multireference configuration interaction and Davidson correction (MRCI+Q) with the spin-orbit coupling (SOC) effect. Spectroscopy constants are fitted and the results are in good agreement with experiments, ensuring the accuracy of the electronic structure. On account of potential energy curves and transition dipole moments, the Franck-Condon factors and Einstein coefficients of transition are obtained. These calculations are used to obtain an accurate partition functions and line lists for molecules. Using the partition functions and line lists, the absorption cross-sections under different temperatures and pressures were simulated. Our work could provide some theoretical insights into solar and cold planet spectrum.