As the key concept in fabricating integrated device, surface plasmon-polaritons (SPPs) have been widely employed to artificially manipulate the electromagnetic waves in metallic surfaces. However, due to the highly structure-dependent resonance of SPPs, it is challengeable to develop a fixed device which can function at wide band. Here, we propose a novel broadband and robust SPPs directional coupler based on the tri-layered curved waveguides working at terahertz (THz) frequencies, where the coupling of SPPs between the adjacent waveguides can be modeled with coupled mode theory. By introducing the stimulated raman adiabatic passage quantum control technique, we achieve the complete transfer of SPPs from the input to the output waveguides in the range of 0.9-1.3 THz, and even considering the propagation loss, the transfer rate is still above 70%. Furthermore, the performance of our device is eminently robust because of its insensitivity to the geometry of structure and the wavelength of SPPs. As a result, our device can tolerate defect induced by fabrication processing and manipulate THz waves at broadband. This finding provides a new theoretical guideline in promoting THz on-demand applications, which is of significance in developing integrated THz devices.