We propose a new structure of high-quality few-mode core and tapered single-mode core to design a six-spatial-mode multiplexer with operating widthband. Using the finite element method(FEM) and the beam propagation method(BPM), the influence of various parameters on the mode coupling effect is studied. By optimizing the parameters, efficient mode coupling effect and good tolerance ability are obtained. Numerical calculation results show that the average coupling efficiencies of the LP11(LP11a and LP11b), LP21(LP21a and LP21b) and LP02 modes in the mode multiplexer are all greater than 90% in the S+C+L band. The core-related parameters have good tolerance, which will greatly reduce the difficulty of device fabrication. The designed mode multiplexer can be applied to MDM system to solve the problem of fiber capacity limitation.