Variable selection techniques for the classical linear regression model have been widely investigated. Variable selection in fully nonparametric and additive regression models has been studied more recently. A Bayesian approach for nonparametric additive regression models is considered, where the functions in the additive model are expanded in a B-spline basis and a multivariate Laplace prior is put on the coefficients. Posterior probabilities of models defined by selection of predictors in the working model are computed, using a Laplace approximation method. The prior times the likelihood is expanded around the posterior mode, which can be identified with the group LASSO, for which a fast computing algorithm exists. Thus Markov chain Monte-Carlo or any other time consuming sampling based methods are completely avoided, leading to quick assessment of various posterior model probabilities. This technique is applied to the high-dimensional situation where the number of parameters exceeds the number of observations. extcopyright 2013 Elsevier B.V. All rights reserved.