In this paper, we make some breakthroughs in the consistency of Tweedie’s compound Poisson model with elastic net. We show that under several mild conditions, the tuning parameter λ can be prespecified, which is in the order of √ log(p/α) /n . Besides, we conduct simulations by analyzing an auto insurance claim dataset to illustrate the model applications. The results exhibit Tweedie’s compound Poisson model with elastic net has an outstanding performance in the variable selection and model fitting effect than grouped lasso. Keywords: Lasso; Adaptive lasso; Group lasso; Generalized linear model; Tweedie’s compound Poisson model with elastic net; Moderate deviation; Tuning parameter; Variable selection.