The main objective of this paper is to develop an observer-based synchronization scheme for networked Hindmarsh-Rose neuron models. Regarding synchronization as a state estimation problem, an observer design approach is used for estimating full state dynamics. Stability of the trajectories to be synchronized is determined by utilization of the contraction theory that provides an efficient tool for analyzing convergence of manifolds with respect to each other. Thereupon, a region where contraction of trajectories takes place is determined; therefore the corresponding error dynamics of the model remain in that contracting region. Consequent results are also supported by a numerical simulation example in the end demonstrating the effectiveness of our approach.