In this paper, we present the numerical and experimental demonstration of asymmetric light transmission by a compact photonic crystal (PC) structure, which sustains semi-Dirac cone dispersion. The semi-Dirac point is obtained by exploiting plane-wave expansion method in a rectangular unit cell of a cylindrical dielectric rod, forming a PC structure. The preselected part of the corresponding PC structure is optimized via differential evolution to maximize the transmission efficiency in one direction, and to minimize in the opposite direction. In this regard, finite-difference time-domain method is integrated with the optimization algorithm to numerically design a compact PC structure with asymmetric light transmission effect. The detailed numerical investigation of the optimized PC structure is represented, and the experiments in the microwave regime are performed to verify the numerical results. The experimentally measured transmission efficiency reaches 78% for one direction, whereas in the opposite direction it reduces to 11%. The physical mechanism of asymmetric light transmission is related to differences of the projection of the wave incident from both directions into the eigenmodes of the photonic structure.