We propose a compact linear polarization spectrometer based on the in-fiber polarization-dependent diffraction grating. The beam profile of radiated light of the grating is shaped to be a Gaussian profile to improve the performance of the spectrometer, where the size of the focused light spot is reduced from 44 um to 33 um with the shaped radiation mode of the grating. Based on the experimental results, the proposed spectrometer can achieve 0.05 nm resolution and 115 nm wavelength responding range from 1495 nm to 1610 nm. To verify the performance of the proposed fiber spectrometer, we measure the transmission spectra of an excessively tilted fiber grating, which has a pair of orthogonal polarization transmission spectra. Compared with the traditional measuring method, the proposed fiber spectrometer integrates the polarizing and spectral analyzing functions in the measuring system and achieves the polarization-sensitive spectral analysis, which shows good wavelength consistency and perfect polarization characteristics.