Inspired by the success of least absolute shrinkage and selection operator (LASSO) in statistical learning, we propose an regularized maximum likelihood linear regression (MLLR) to estimate models with only a limited set of adaptation data to improve accuracy for automatic speech recognition, by regularizing the standard MLLR objective function with an constraint. The so-called LASSO MLLR is a natural solution to the data insufficiency problem because the constraint regularizes some parameters to exactly 0 and reduces the number of free parameters to estimate. Tested on the 5k-WSJ0 task, the proposed LASSO MLLR gives significant word error rate reduction from the errors obtained with the standard MLLR in an utterance-by-utterance unsupervised adaptation scenario.