Fano resonance is realized theoretically in a photonic crystal. The structure is composed of a cavity side coupled to a partially transmitting waveguide. By optimizing the structure parameters, asymmetric sharp Fano resonance transmittance spectrum is achieved with quality factor of 2 213, extinction ratio of 57 dB and peak loss of 0.2 dB. The sharp spectrum can be used in sensor applications. Such as pressure sensor, the pressure sensitivity is about 9.15 nm/GPa. and for refractive index sensing application, the sensitivity is about 800 nm/RIU, and the maximum of figure of merit can reach 1 000. Besides, this sharp Fano resonance based on photonic crystal has potential applications in optical switches, filters etc. And it can be integrated into optical communications and optical integration circuits.