In the process of theoretical fitting the switching current distributions of Josephson junction,macroscopic quantum tunneling (MQT) and thermally activated process are usually considered.Analysis of the results for a Bi2Sr2CaCu2O8+δ surface intrinsic Josephson junction (SIJJ), quantum corrections are considered at the intermediate areas between MQT and thermally activated process. It is found that quantum corrections lead to a perfect fit to the experimental data, which may be useful for the future studies of MQT in SIJJs and their possible applications as a superconducting qubit.