We propose and numerically analyze a plasmonic Bragg reflector formed in a graphene waveguide. The results show that the graphene plasmonic Bragg reflector can produce a broadband stopband that can be tuned over a wide wavelength range by a small change in the Fermi energy level of graphene. By introducing a defect into the Bragg reflector, we can achieve a Fabry-Perot-like microcavity with a quality factor of 50 for the defect resonance mode formed in the stopband. The proposed Bragg reflector could be used as a broadband ultrafast tunable integrated filter and a broadband modulator. In addition, the defect microcavity may find applications in graphene-based resonators.