The correspondence ghost imaging scheme via photon counting based on micromirror device is proposed. In this scheme, a digital micromirror device is used to module the light source, the time-correlated single photon counting technology is introduced to acquire the photon counting value, and correspondence ghost imaging is used to calculate the image of target object. The principle of correspondence ghost imaging via photon counting is clarified with ghost imaging theory and correspondence ghost imaging theory, and the proposed scheme is verified by experiments. The research results show that the proposed scheme can realize weak light imaging. The images achieved by the proposed scheme are as good as those by traditional ghost imaging while the computational complexity in the process of image reconstruction is reduced. Besides, the measurement of intensity distribution by array detector is omitted in the proposed scheme and the image of target object is acquired with a single photon detector which has no spatial resolution, combined with correspondence ghost imaging algorithm. In the meantime, the proposed scheme can provide distance information of the object.