We demonstrate a novel fiber tip Fabry-Perot (FP) interferometer with a chirped spectral characteristic. The FP interferometer is formed by an etched chirped fiber Bragg grating (FBG) and the fiber tip broadband end-face mirror, and the etched chirped FBG is prepared by a dynamic chemical etching process, shaping the taper and reducing the size from 125 μm to just a few micrometers. Due to the spectral characteristic of the etched chirped FBG, the different resonance wavelengths correspond to different gating positions which give rise to the gradient cavity length in the chirped fiber tip FP interferometer; thus, this FP interferometer possesses a chirped interference spectrum. Subsequently, the FP interferometer is fabricated, and the temperature response is investigated by measuring the wavelength shift of the resonance dips in the reflection spectrum. Significantly, because of its special interference principle and configuration, we experimentally demonstrate that this FP interferometer can be used for the spatial localization of the external temperature perturbations.