A long-period fiber-grating sensor with a high strain sensitivity of -7.6 pm/microepsilon and a low temperature sensitivity of 3.91 pm/ degrees C is fabricated by use of focused CO(2) laser beam to carve periodic grooves on a large- mode-area photonic crystal fiber. Such a strain sensor can effectively reduce the cross-sensitivity between strain and temperature, and the temperature-induced strain error obtained is only 0.5 microepsilon/ degrees C without using temperature compensation.