In this paper, we propose and analytically demonstrate a biosensor configuration based on the excitation of surface electromagnetic waves in a graphene-based one-dimensional photonic crystal (1D PC). The proposed graphene-based 1D photonic crystal consists of alternating layers of high (graphene) and low (PMMA) refractive index materials, which gives a narrow angular reflectivity resonance and high surface fields due to low loss in PC. A differential phase-sensitive method has been used to calculate the sensitivity of the configuration. Our results show that the sensitivity of the proposed configuration is 14.8 times higher compared to those of conventional surface plasmon resonance (SPR) biosensors using gold thin films. This novel and effective graphene-based 1D PC will serve as a promising replacement of metallic thin film as a sensor head for future biosensing applications.