The angle between slant and azimuth axes is 45 degrees in slant-mount telescopes, which use the slant rotation to replace altitude movement in traditional mounts. The circular motion can achieve more smooth driving in altitude direction, and can effectively overcome problems in traditional mounts such as vibrations around the zenith. It is a hot topic in researches of current astronomical instruments. While the vertical displacement of the structure is composed by circle rotation of the slant axis, which causes displacements of the two direction coupled. Moreover, the slant rotation can also leads to the revolving movement of CCD images of the tracking system. These two problems bring great challenges to the slant mount driving. In this paper, based on a slant mount, we establish accurate mathematical model of the drive system to effectively compensate for the revolving movement of the image field, decompose in real time the deviation of vertical and horizontal directions by the decoupling algorithm, and design the control system using FPGA to carry out testing experiments. We strive to solve the displacement coupling and the image revolving movement problem, and thus provide a feasible technical support for driving control of slant mounts.