The cross phase (CP) opens up a new horizon for the generation and measurement of vortex beams, and the conversion between Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes can be done with a CP. However, the conversion plane is in the far plane, and the width cannot be adjusted. In this article, we present a more convenient and practical mode converter between HG and LG modes based on CP combined with a lens. The feasibility of the converter for the conversion between two modes is theoretically analyzed. The conversion can be accomplished in the determined plane and the width of converted beam can be controlled by adjusting the parameter of converter. Proof-of-concept experiment is carried out to verify theoretical analysis and the experimental results are agree well with theoretical simulations. The transfer of orbital angular momentum (OAM) between two modes after passing through the converter is also analyzed. From the perspective of OAM conservation, the required parameter conditions for the converter are discussed. In principle, such a converter as proposed here might even be applied to microwave, millimeter wave, and terahertz OAM fields.