We propose a new group variable selection and estimation method, and illustrate its application for the generalized linear model (GLM). This new method, termed “gMIC”, was derived from approximating the information criterion by a smooth unit dent function. The gMIC is derived as a smooth approximation of a group-version modification of the information criterion. The approximated information criterion is further reparameterized in a way that not only renders sparse estimation from a smooth programming problem but also facilitates a convenient way of circumventing post-selection inference. Compared to existing group variable selection and estimation methods, the gMIC is free of parameter tuning and hence computationally advantageous. We also establish the oracle property of the proposed method that is supported by both simulation studies and real examples.