Generalized additive model(GAM) is the statistical model that resolves most of the problems existing in the traditional linear regression model. However, overfitting phenomenon can be aroused without applying any method to reduce the number of independent variables. Therefore, variable selection methods in generalized additive model are needed. Recently, Lasso related methods are popular for variable selection in regression analysis. In this research, we consider Group Lasso and Elastic net models for variable selection in GAM and propose an algorithm for finding solutions. We compare the proposed methods via Monte Carlo simulation and applying auto insurance data in the fiscal year 2005. lt is shown that the proposed methods result in the better performance.