EEG source reconstruction is a challenging task and several methods have been applied to this ill-posed inverse problem. Most of the reconstruction techniques rely on imaging models, where the neural activity is described by a dense set of current dipoles. On the other hand, the point source models, which employ a small number of equivalent current dipoles, has received less attention. While both approaches (imaging versus current dipoles) have their own issues, the main advantage of the dipole models is that they approximate summaries of evoked responses or helpful first approximations. In this paper, we use a recursive Bayesian estimation technique, known as Particle Filter (PF), to simultaneously reconstruct the spatial locations within the head and the corresponding waveforms of the most active dipoles that originated the EEG sensor data. Normally, in EEG source reconstruction, fixed dipole locations are assumed. The proposed PF framework presents a shift in the current paradigm by estimating moving EEG sources, which may vary from one location to another in the brain reflecting the underlying brain activity. Our computer simulations, based on generated and real EEG data, show that the proposed PF approach estimates the dynamic EEG sources with high fidelity.