Zero-inflated count models have received considerable amount of attention in recent years, fuelled by their widespread applications in many scientific disciplines. In this paper, we consider the problem of selecting grouped variables in zero-inflated Poisson (ZIP) models via group bridge regularization. The ZIP mixture likelihood with a group-wise penalty on the coefficients is formulated using least squares approximation and then the parameters involved in the penalized likelihood are estimated by an efficient group descent algorithm. We examine the effectiveness of our modeling procedure through extensive Monte Carlo simulations. An auto insurance claim dataset from the SAS Enterprise Miner database is analyzed for illustrative purposes. Finally, we derive theoretical properties of the proposed group variable selection procedure under certain regularity conditions. The open source software implementation of this method is publicly available at https://github.com/himelmallick/Gooogle.