In this paper, a novel broadband all-fiber mode converter is proposed and experimentally demonstrated. Through writing a pair of superimposed long period fiber gratings (SLPFGs) in tow-mode fiber (TMF) with a CO2 laser, the mode converter can realize the conversion from LP01 to LP11 owing to the phase matching condition. Numerical and experimental results show that the bandwidth of this mode converter is 3 times broader than that of a single grating converter. The converter has low loss, high coupling efficiency, small size and is easy to fabricate, so it can be widely used in mode-division multiplexing.