We demonstrate the fabrication of a long-period fiber grating (LPFG) in a boron-doped single-mode fiber with a high-diffractive-order cladding mode (HDCM) near the turning point (TP). The simulations show that an LPFG with less than 0.2 duty cycles can couple light to the HDCM. An LPFG with a period of more than 400 μm can achieve strong mode coupling between the fundamental mode and the HDCM near the TP. The effect of the external refractive index on the transmission spectrum of a LPFG with different grating periods is investigated by simulations and experiments. With an increase in grating period, the spectral dip corresponding to the HDCM travels faster than the conventional dip, and overlapped dips appear in the transmission spectrum. High sensitivities of up to 13,497.7 nm/RIU and 0.77 nm/°C of, respectively, RI and temperature sensing can be achieved. Such LPFGs could be potentially used as optical filters and high-sensitivity sensors.