Coupled-waveguide devices are essential in photonic integrated circuits for power coupling, polarization handling and mode manipulation. However, the performance of these devices usually suffers from high wavelength and structure sensitivity, which makes it challenging to realize broadband and robust on-chip optical functions. Here, we propose and experimentally demonstrate broadband on-chip mode manipulation with very large fabrication tolerance based on the Thouless pumping mechanism. Thanks to such a topological scheme, the mode conversion and multiplexing show a broad bandwidth of 80 nm and remarkable fabrication tolerance of ±70 nm for the structural deviations in waveguide width and gap distance, which is, to the best of our knowledge, the highest fabrication tolerance among the coupled-waveguide mode-handling devices reported so far. As a proof-of-concept experiment, we build a four-channel mode-division multiplexer based on the topological waveguide arrays and demonstrate the transmission of 200-Gb/s 16-quadrature amplitude modulation (16-QAM) signal for each channel, which validates the feasibility of applying topological photonic devices in practical communication systems. This work reveals the possibility of developing new classes of broadband and fabrication-tolerant coupled-waveguide devices with topological photonic approaches, which may find applications in many fields including optical interconnects, quantum communications, optical computing and beyond.