The compressive sensing has been applied to develop an effective framework for simultaneously localizing multiple targets in wireless sensor networks. Nevertheless, existing methods implicitly use analog measurements, which have infinite bit precision. In this letter, we focus on off-grid target localization using quantized measurements with only several bits. To address this, we propose a novel localization framework for jointly estimating target locations and dealing with quantization errors, based on the novel application of the variational Bayesian Expectation-Maximization methodology. Simulation results highlight its superior performance.