The structure of asymmetric LPFG with rotary refractive index modulation （R-LPFG） along the fiber axis is proposed and fabricated by using high frequency CO2 laser pulses. The transverse refractive index distribution of LPFG with asymmetric refractive index modulation in the cross-section is divided into multilayer circular waveguides, which are then discretized according to the magnitude of index. The mode coupling characteristics of this asymmetric LPFG is discussed by adopting coupled-mode equation sets and the revised Bragg condition. It’s observed that the transmission spectrum has different features depending on the rotation angle. For small angles, resonance peak is unique, however, when the angle becomes greater, the resonance peak will be split into two, which is different from the transmission spectrum of previous LPFGs. Moreover, the two split peaks have almost the same temperature sensitivity because they originated from the same two coupling modes. The high sensitivity torsion meter and strain meter without temperature compensation can be designed by adopting the wavelength spacing between the two split peaks.