In this paper, we consider a class of semiparametric additive models where both.nonparametric additive component and parametric component present.A variable selection method combining the penalized least square and backfitting algorithm is developed to select significant variables for the parametric portion.We establish the rate of convergence as well as the asymptotic normality for the resulting estimator and demonstrate that the proposed method enjoys the sparsity and oracle properties.Furthermore, the one-step algorithm is applied to reduce the computational burden.On the other hand, the generalized likelihood ratio test with the help of backfitting algorithm is applied to select significant variables in the nonparametric component.We show that the limiting distribution of the test statistic follows a chi-square distribution, which implies that the Wilks phenomenon holds.Some Monte-Carlo simulations are provided to illustrate the performance of the proposed methods.