Large datasets, where the number of predictors p is larger than the sample sizes n, have become very popular in recent years. These datasets pose great challenges for building a linear good prediction model. In addition, when dataset contains a fraction of outliers and other contaminations, linear regression becomes a difficult problem. Therefore, we need methods that are sparse and robust at the same time. In this paper, we implemented the approach of MM estimation and proposed L1-Penalized MM-estimation (MM-Lasso). Our proposed estimator combining sparse LTS sparse estimator to penalized M-estimators to get sparse model estimation with high breakdown value and good prediction. We implemented MM-Lasso by using C programming language. Simulation study demonstrates the favorable prediction performance of MM-Lasso.