In this paper, a new method based on LASSO algorithm is studied for the estimation of stellar alpha element abundance. The information of alpha elements (O, Mg, Ca, Si, and Ti) of massive stars will help us to better understand the evolution of the galaxy. Presently the main method of determining the alpha element abundances from the low resolution spectra is the template matching method. However, it is difficult for us to optimize the algorithm parameters and the algorithm is sensitive to the noise. Thus, it is necessary to study the new method to determine the abundance. The experimental results show that the accuracy of LASSO algorithm on ELODIE spectra is 0.003 (0.078) dex. To explore the impact of the spectral resolution variation, we use ELODIE spectra to generate the spectral data sets with following resolutions: 42 000, 21 000, 10 500, 4 200 and 2 100 by using the Gaussian convolution. The results of the LASSO algorithm on these data sets are 0.003 3 (0.078) dex, -0.05 (0.059) dex, -0.007 (0.069) dex and -0.004 5 (0.067) dex, respectively. These results show that the LASSO algorithm is not sensitive to the change of the resolution. In order to verify the robustness of LASSO algorithm against the change of SNRs, we use ELODIE to generate the spectral data sets with following SNRs: 30, 25, 20, 15 and 5. The results of LASSO algorithm on the above data sets are: -0.002 (0.076) dex, -0.090 (0.073) dex, 0.003 6 (0.075) dex, 0.007 6 (0.078) dex and -0.009 (0.080) dex, respectively. Thus, LASSO algorithm is not sensitive to the change of SNR. Therefore, the LASSO algorithm is suitable for low resolution and low SNR spectra such as LAMOST and SDSS spectra. The accuracy of Lasso algorithm on the SDSS spectra is 0.003 7 (0.097) dex, and the results of LASSO on globular and open clusters show good agreement with literature values (within 1σ). Therefore, the LASSO algorithm can be used to estimate the alpha element abundances of stars.