In this study, a novel dual-core photonic crystal fiber sensor based on surface plasmon resonance is proposed for cancer detection in various parts of the human body. The proposed sensor is designed with a simplified circular geometrical structure with two different sizes of air holes. A gold thin film is placed on the on the cladding of the photonic crystal fiber. The performance of the proposed sensor is demonstrated by applying full vectorial finite element method. The confinement loss and amplitude sensitivity are calculated for the different normal and cancer cells. The proposed sensor has the amplitude sensitivity 595 RIU-1 for the skin cancer and wavelength sensitivity 16,285 nm/RIU for the Adrenal Gland cancer. Furthermore, the proposed cancer sensor achieved the highest Figure of Merit of 571.4 RIU-1. The numerical results indicate that the suggested biosensor could detect cancer cells. Finally, we investigate the fabrication tolerance on the confinement loss and amplitude sensitivity.