An improved orthogonal matching pursuit (OMP) algorithm is proposed to solve signal loss problem of the fiber Bragg grating (FBG) sensing signal with external disturbances. Based on the essential characteristics of the wavelength drift of FBG sensing signals with stress, within the framework of compressive sensing theory, the effective sparsity of FBG signal was obtained by removing the imaginary part of sparsity coefficient and applying exponential saturation method fitting and ranking the non-zero elements. Moreover, by improving the atom selection strategy and the termination conditions in the iteration process of the traditional OMP algorithm, the complexity of algorithm was reduced and the reconstruction accuracy of the signal was improved. The results of the comparative experiments demonstrate that the proposed algorithm has outstanding advantages on time complexity, signal noise ratio (SNR) and reconstruction accuracy.