The high-pressure structures of an underdoped cuprate superconductor Bi2Sr2CaCu2O8+delta have been studied by synchrotron X-ray diffraction at pressures up to 36.5 GPa. We find that this superconductor retains its orthogonal structure with the space group Amaa in the pressure range studied. Upon compression, both the a and b axes first shrink monotonically up to 17.4 GPa from their ambient pressure values and keep these behaviors with positive compressibilities up to 36.5 GPa after experiencing expansion with negative compressibilities in the pressure regime between 17.4 and 23.7 GPa. However, the c axis decreases continuously with increasing pressure with a slow change at about 23.7 GPa. The results indicate an isostructural phase transition starting at 17.4 GPa and a structural collapse at around 23.7 GPa.