Ion mobility spectrometry (IMS) is a rapid, highly sensitive analytical method for the gaseous samples with a low detection limit. It is widely used to detect chemical warfare agents, illegal drugs and explosives. The original spectrum contains not only sample information, but also noise. Especially when the concentration of the analyte is low, the accuracy of qualitative and quantitative analysis based on IMS technology is seriously influenced. It is necessary to reconstruct the spectrum before qualitative and quantitative analysis. In our article, a new method simultaneously achieved the spectrum reconstruction, and characteristic peaks extraction was proposed. In the optimization function, we chose l1 norm as the linear penalty. The regularization parameter λ was used to adjust the scale of the penalty in the optimization. Solve the optimization function, a Gaussian dictionary was constructed to represent the shape of peak firstly, and the surrogate function algorithm was adopted to solve it. When the root mean squared error between the reconstructed and original spectrum achieved the set threshold, the algorithm was stopped. To evaluate the performance of our method proposed, the simulated data set and DMMP sample data set were used. The simulated data set was composed of Gaussian functions and Gaussian noise. Meanwhile, we compared our method with wavelet using a soft threshold, wavelet using hard threshold and S-G smoothing methods. Root mean squared error(RMSE) and signal to noise ratio(SNR) were used to compare the results of different methods. The experiments results show that our method has significant improvement than other methods. Based on the proposed method, qualitative and quantitative analysis can be carried out.