In this work, we present a theoretical model of a near-infrared sensitive refractive index biosensor based on the truncate 1D photonic crystal (1D PC) structure with Dirac semimetal. This highly sensitive near-infrared biosensor originates from the sharp reflectance peak caused by the excitation of Bloch surface wave (BSW) at the interface between the Dirac semimetal and 1D PC. The sensitivity of the biosensor model is sensitive to the Fermi energy of Dirac semimetal, the thickness of the truncate layer and the refractive index of the sensing medium. By optimizing the structural parameters, the maximum refractive index sensitivity of the biosensor model can surpass 17.4 × 10³/RIU, which achieves a certain competitiveness compared to conventional surface plasmon resonance (SPR) or BSW sensors. Considering that bulk materials are easier to handle than two-dimensional materials in manufacturing facilities, we judge that 3D Dirac semimetal and its related devices will provide a strong competitor and alternative to graphene-based devices.