The compact alternating direction implicit (ADI) scheme for two-dimensional Caputo-Hadamard fractional sub-differential equations is studied. Firstly, the Caputo-Hadamard fractional derivative on exponential type meshes is approximated. Secondly, in order to solve the high-dimensional problems, a compact ADI method is proposed. With the help of mathematical induction and the properties of discrete coefficients, the stability and convergence of the proposed scheme are analyzed. Ultimately, an example is presented to show the effective of our analysis.