A novel broadband LP01↔LP02 mode converter for dispersion compensation based on special dual-core fiber is theoretically investigated by using the coupled-mode theory. The simulated mode converter has ∼22 nm bandwidth with a conversion efficiency of over 80%. Furthermore, this noncomplete conversion only introduces the insertion loss rather than multipath interference resulting from the residual LP01 mode. Finally, one optimal scheme for broadening the bandwidth of high-efficiency conversion has been proposed by longitudinally tapering the dual-core fiber. The simulation results show that the conversion bandwidth can be improved to ∼31 nm by tapering with a scaling range of only 2%.