A quasi-D-shaped photonic crystal fiber plasmonic sensor with a rectangular lattice is proposed by using Au as a plasmonic layer and graphene to enhance the sensing performance. By moving the core to the edge of the fiber, a shorter polishing depth is achieved, which makes the fiber proposed have a greater mechanical strength than other common D-shaped fibers. Benefiting from the natural advantage of the rectangular lattice, the dual sensing channels make the proposed sensor show a maximum wavelength interrogation sensitivity of 3877 nm/RIU with the dynamic refractive index range from 1.33 to 1.42 and a maximum amplitude sensitivity of 1236 RIU−1 with the analyte RI = 1.41 in the visible region. The corresponding resolutions are 2.58 × 10−5 and 8.1 × 10−6 with the methods of the wavelength interrogation method and amplitude- or phase-based method. These advantages make the proposed sensor a competitive candidate for biosensing in the field of refractive index detection, such as water quality analysis, clinical medicine detection, and pharmaceutical testing.