A measurement system is developed to observe the switching current distribution in Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions (IJJ's). We have designed the frequency responses of filters and cables to achieve the compatibility of sufficient isolation at high frequency region and accurate detection of the distribution at low frequency region. The temperature dependence of the switching current distributions measured on a IJJ by the present system agrees well with the theoretical calculation in the temperature range from 70 mK to 5 K. The consistency of the crossover temperature between experimental result and calculation suggests that the designed measurement system succeeded in observing the macroscopic quantum tunneling process.