In this paper, we report a novel long-period fiber grating (LPFG) fabricated by using a new writing technique that is mainly based on the thermal shock effect of focused high-frequency CO2 laser pulses at several kilohertz. A number of unique characteristics of such a LPFG, such as bend, torsion, and transverse load, are observed by experiments, for the first time, to our knowledge. Based on these unique features, a novel bend-insensitive LPFG sensor that could solve the problem of cross-sensitivity between bend and other measurands, a novel torsion sensor that can realize absolute measurement of twist rate, and a load sensor that can achieve simultaneous measurement of transverse load and temperature using a single LPFG element are proposed and demonstrated. These unique features of the LPFGs are mainly due to the asymmetrical distribution of the refractive index on the cross section of the LPFG induced by high-frequency CO2 laser pulses.