This study developed a novel acoustic emission (AE) tomography algorithm for non-destructive testing (NDT) based on Lasso regression (LASSO). The conventional AE tomography method takes considerable measurement data to obtain the elastic velocity distribution for structure evaluation. However, the new algorithm in which the LASSO algorithm is applied to AE tomography eliminates these deficiencies and reconstructs equivalent velocity distribution with fewer event data to describe the defected range. Three numerical simulation models were studied to reveal the capacity of the proposed method, and the functional performance was verified by three different types of classical concrete damage numerical simulation models and compared to that of the conventional SIRT algorithm in the experiment. Finally, this study demonstrates that the LASSO algorithm can be applied in AE tomography, and the shadow parts are eliminated in resultant elastic velocity distributions with fewer measurement paths.