Mode-division multiplexing (MDM), as one of the promising techniques for overcoming current limitation of transmission capacity in single-mode fibers (SMFs), has attracted considerable attention. A key component in the MDM system is a mode converter, which makes conversion between the fundamental mode and the higher-order mode. Many mode converters have been demonstrated, such as spatial light modulators, phase plates, silicon-based asymmetrical directional couplers, fiber-based photonic lantern, and long period fiber grating (LPFG). Compared with other methods, mode converter used LPFG is a very feasible technique, which has the advantages of small size, low loss, low backward noise, high coupling efficiency and easy fabrication. However, the limitation of the mode converter is relatively narrow bandwidth. In this paper, a novel broadband all-fiber mode converter is proposed, in which two long period fiber gratings (LPFGs) with different periods are fabricated in the same spatial domain of few-mode fiber to achieve coupling from LP ₀₁to LP ₁₁, thus forming superimposed long period fiber gratings (SLPFGs). The influences of grating parameters, such as the interval between two periods, the length of grating and the coupling coefficient on the mode converter, are analyzed by numerical simulation. It is found that the gap between the two resonant wavelengths becomes smaller with the periodic interval decreasing, which can form one rejection band when the gap is small enough, thus a broadband mode converter can be realized. The corresponding bandwidth at a conversion efficiency of 10 dB is about twice that of traditional LPFG. Moreover, with the increase of grating length, the conversion efficiency first increases and then decreases, because coupling efficiency experiences deficient coupling, full coupling and over coupling. The effect of coupling coefficient on converter is similar to that of grating length. According to the numerical results, grating I is fabricated with ${\varLambda _1} = 673\;{\text{μ}}{\rm m} $ , 35-period. After that, the platform is rotated 180° and grating II is fabricated with ${\varLambda _2} = 688\; {\text{μ}}{\rm m}$ , 35-period by CO ₂laser in tow mode fiber (TMF steped-index fiber). The bandwidths of both LPFGs at a conversion efficiency of 10 dB are about 57 nm and 67 nm respectively, while the bandwidth of SLPFG is about 153 nm. The experimental results are in pretty good agreement with the theoretical analyses. In addition, the proposed superimposed structure can also be extended to the conversion of fundamental mode into other high-order core modes. By designing the period of two sub-gratings reasonably, a wide band rejection filter with arbitrary wavelength can be realized. Compared with the traditional mode converter, the converter has the advantages of broad bandwidth, high conversion efficiency and small size, which can be widely used in the mode division multiplexing system and optical communication.