Herein, we investigated the pressure dependence of electric transport in a new type of superconducting metal iridate compound, SrIr2, that exhibits a superconducting transition temperature, T-c, as high as 6.6 K at ambient pressure, in order to complete the T-c-pressure (p) phase diagram. Very recently, this sample's superconductivity was discovered by our group, but the superconducting behavior has not yet been clarified under pressure. In this study, we fully investigated this sample's superconductivity in a wide pressure range. The T-c value decreased with an increase in pressure, but the onset superconducting transition temperature, T-c(onset), increased above a pressure of 8 GPa, indicating an unconventional superconductivity different from a BCS-type superconductor. The magnetic field dependence of electric resistance (R) against temperature (R - T plot) recorded at 7.94 and 11.3 GPa suggested an unconventional superconductivity, followed by a p-wave polar model, supporting the deviation from a simple s-wave pairing. Moreover, we fully investigated the pressure dependence of crystal structure in SrIr2 and discussed the correlation between superconductivity and crystal structure. This is the first systematic study on superconducting behavior of a new type of metal iridate compound, MIr2 (M: alkali-earth metal atom), under pressure.