Compared with FBG, long period fiber gratings (LPFGs) have higher sensing sensitivity in many aspects. With the development of few-mode fiber (FMF), few mode long period fiber gratings (FM-LPFGs) has grasped a lot of research focus in recent years. The co-propagating coupling between a core mode and a cladding mode, or two different core modes, will bring different effects on the sensing characteristics of temperature, strain and refractive index. However, the coupling characteristics between core modes and cladding modes have been rarely reported in theory before. In this paper, based on the coupled-mode theory, we simulate the transmission spectrum of the FM-LPFGs by use of MATLAB and COMSOL software. Assuming that all the power is launched in a certain mode, we calculate the coupling coefficients and the transmission spectrums between the core modes (LP01, LP11, LP21, and LP02) and the cladding modes LPlm (l=1) at 1550nm. In addition, we change some fiber parameters like grating period, refractive index modulation depth and cladding diameter to analyze their effect on the transmission spectrum. Based on the simulation, we fabricate some FM-LPFGs by the CO2 laser, and use them in temperature sensing experiments. With the certain strain, we measured the temperature sensing sensitivity of the FM-LPFGs. The measured sensitivities of temperature is -43.98pm/°C.