Magnetic resonance electrical impedance tomography (MREIT) is a recently introduced noninvasive conductivity imaging modality, which combines the magnetic resonance current density imaging (MRCDI) and the traditional electrical impedance tomography (EIT) techniques. MREIT is aimed at providing high-spatial-resolution images of electrical conductivity because it avoids solving the well-known ill-posed problem in the traditional EIT. In this article, we review our research activities in MREIT imaging of head-brain tissue conductivity profiles. We have developed several imaging algorithms and conducted a series of computer simulations for MREIT imaging of the head-brain tissues. Our work suggests that MREIT brain imaging may become a useful tool in imaging conductivity distributions of the brain and head.