The longitudinal momentum distributions of the core-like fragment 7Be from the breakup of 8B on 12C target have measured at the energy of 36MeV/u at the Radioactive Ion Beam Line in Lanzhou (RIBLL). In order to distinguish the stripping and diffraction mechanisms involving in breakup reaction of 8B, both fragments of 7Be and proton are measured coincidently. With this coincident measurement, the widths of longitudinal momentum distribution are deduced with the values of 124±17MeV and 92±7 MeV for stripping and diffraction mechanism respectively. It is found that the longitudinal momentum width of stripping component is larger than that of diffraction component, which is different from the breakup reaction at high energy as around GeV/u. The theoretical calculations are compared with these experimental results.