The joint Fresnel transform correlator is achieved by using a phase-only spatial light modulator to encode linear phase mask. Under the illumination of monochromatic plane wave, the reference image and the target image are modulated by the linear phase mask. In the plane where Fresnel diffraction field centers are superimposed, the joint Fresnel transform power distribution (JFTPD) of the reference image and the target image can be recorded with a CCD camera. The JFTPD is input to the optical Fourier inverse transform system, and the correlation spots can be obtained in the output plane after Fourier inverse transform. The results of numerical simulations and experiments show that the correlator can output sharp correlation peaks, and the correlation peak values are sensitive to the relative position of the reference image and the target image. When the distance between the reference image and the target image changes by -30 pixel and +40 pixel, the correlation peak value decreases to 23% and 48% respectively.