A mode multiplexer/demultiplexer (MUX/DeMUX) is a crucial component for constructing mode-division multiplexing (MDM) systems. In this paper, we propose and experimentally demonstrate a wide-bandwidth and highly-integrated mode MUX/DeMUX based on an inverse-designed counter-tapered coupler. By introducing a functional region composed of subunits, efficient mode conversion and evolution can be achieved, greatly improving the mode conversion efficiency. The optimized mode MUX/DeMUX has a size of only 4 µm × 2.2 µm. An MDM-link consisting of a mode MUX and a mode DeMUX was fabricated on the silicon-on-insulator (SOI) platform. The experimental results show that the 3-dB bandwidth of the TE fundamental mode and first-order mode can reach 116 nm and 138 nm, respectively. The proposed mode MUX/DeMUX is scalable and could provide a feasible solution for constructing high-performance MDM systems.