Traditionally, connected vehicles (CVs) share their own sensor data that relies on the satellite with their surrounding vehicles by vehicle-to-vehicle (V2V) communication. However, the satellite-based signal sometimes may be lost due to environmental factors. Time-delays and packet dropouts may occur randomly by V2V communication. To ensure the reliability and accuracy of localization for CVs, a novel variational Bayesian (VB)-Kalman method is developed for unknown and time varying probabilities of delayed and lost measurements. In this VB-Kalman localization method, two random variables are introduced to indicate whether a measurement is delayed and available, respectively. A hierarchical model is then formulated and its parameters and state are simultaneously estimated by the VB technique. Experimental results validate the proposed method for the localization of CVs in practice.