A common approach to the electroencephalogram (EEG) source localization problem is to estimate the states of current dipoles. However, the dipole estimation problem is difficult because not only is it an inverse problem but also the number of dipoles can change over time. In this paper, we model the relationship between current dipoles and EEG observations using a state-space model where the creation and annihilation of dipoles is represented as a birth-death process. We estimate the dipoles' positions and moments with a Rao-Blackwellized particle filter and estimate whether a new dipole has been created or an existing one annihilated via the Bayesian information criterion. Experiments on both synthetic and real data show that the proposed model and estimation method can effectively estimate the number and positions of the dipoles.