By using a graded-index multimode fiber (GI-MMF) with a relatively flat index profile and high refractive index of the fiber core, a microextrinsic fiber-optic Fabry?P′erot interferometric (MEFPI) strain sensor is fabricated through chemical etching and fusion splicing. Higher reflectance of the microcavity is obtained due to the less-curved inner wall in the center of the fiber core after etching and higher index contrast between the GI-MMF core and air. The maximum reflection of the sensor is enhanced 12 dB than that obtained by etching of the Er- or B-doped fibers. High fringe contrast of 22 dB is obtained. The strain and temperature responses of the MEFPI sensors are investigated in this experiment. Good linearity and high sensitivity are achieved, with wavelength-strain and wavelength-temperature sensitivities of 7.82 pm/\mu \varepsilon and 5.01 pm/?C, respectively.