Based on the status that the existing grating spectrum demodulation methods require large amount of data which limited the data transformation and processing, compressed sensing is introduced to reconstruct high-precision grating spectrum through acquiring a few spectrum data. Fiber Bragg grating (FBG) and linearly chirped fiber Bragg grating (LCFBG) are selected as the research objects. Grating spectrum FBG calibration experiment platform is built with tunable Fabry-Perot (F-P) filter demodulation algorithm (TFPDA) as the reference to validate the reconstructing practicability of compressed sensing. Gaussian nonlinear curve fitting is utilized to extract the center wavelengths reconstructed by TFPDA and compressed sensing under different temperatures. TBG temperature sensitivity coefficient obtained by compressed sensing is 20.3 pm/℃. Compared with the coefficient obtained by TFPDA, the relative error is 0.5%. Comparative analysis of LCFBG spectra collected by these two methods, the maximum error in 3 dB bandwidth is 1.03% and center wavelength is 0.69%. All these experimental results confirm that compressed sensing has certain application value in grating spectrum acquisition and reconstruction.