An all-fiber LP02 broadband mode converter is proposed in this paper. Boardband is achieved when LP01 mode is converted to LP02 mode by using LP11 mode as an intermediate mode based on the mode matching principle and the designed dual-core fiber. The relationship between fiber parameters and the effective index was investigated as well as structure parameters and conversion bandwidth, and the structure is optimized by using the beam propagation method and the mode coupling theory. The bandwidth is compared of the method convert LP01 mode to LP02 mode directly with the method using LP11 mode as an intermediate mode. Simulation results show that the intermediate method can improve the bandwidth and conversion bandwidth can reach 121nm with a conversion efficiency over 80%.