We demonstrate the fabrication of long-period fiber gratings (LPFGs) written in the two-mode fiber (TMF) by CO2 laser. Both uniform and tilted LPFGs were fabricated to provide the light coupling between LP01 mode and LP11 mode with a coupling efficiency of more than 99%. The writing efficiency and the bandwidth of the LPFG mode converter can be adjusted by changing the tilt angle of the tilted TMF-LPFGs. The torsion sensitivity of conventional and tilted LPFG mode converters were measured to be 0.37 nm/(rad/m) and 0.50 nm/(rad/m), respectively. Two orthogonal vector modes (the HEeven 21and HEodd 21 modes) and corresponding orbital angular momentum state were successfully obtained at the resonance wavelength. The proposed LPFG mode converter could be used as not only a high efficiency wavelength tunable mode converter in the mode division multiplexing system but also a high sensitive torsion sensor in the field of optical sensing.