We studied the electronic and vibrational properties of monazite-type SrCrO4 under compression. The study extended the pressure range of previous studies from 26 to 58 GPa. The existence of two previously reported phase transitions was confirmed at 9 and 14 GPa, and two new phase transitions were found at 35 and 48 GPa. These transitions involve several changes in the vibrational and transport properties with the new high-pressure phases having a conductivity lower than that of the previously known phases. No evidence of chemical decomposition or metallization of SrCrO4 was detected. A tentative explanation for the reported observations is discussed.