By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts of R2 line, and U band of GSGG:Cr3+ at 300 K have been calculated, respectively. The calculated results are in good agreement with all the experimental data. Their physical origins have also been explained. It is found that the mixingdegree of 22(3T1)e4T2> and 322E> base-wavefunctions in the wavefunctions of R1 level of GSGG:Cr3+ at 300 K is remarkable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the and the PS of R1 line (or R2 line) due to EPI are quite different. It is the combined effect of them that gives rise to the total PS ofR1 line (or R2 line). In the range of about 15 kbar ～ 45 kbar, the mergence and/or order-reversal between t22(3T1)e4T2 levels and t32 2 T1 levels take place, which cause the fluctuation of the rate of PS for t22(3T1)e4T2 (or t3 2 2T1)with pressure. At 300 K, both the temperature-dependent contribution to R1 line (or R2 line or U band) from EPI and the temperature-independent one are important.