Recently, an end-to-end MR image reconstruction technique, called AUTOMAP, was introduced to simplify the complicated reconstruction process of MR image and to improve the quality of reconstructed MR images using deep learning. Despite the benefits of end-to-end architecture and superior quality of reconstructed MR images, AUTOMAP suffers from the large amount of training parameters required by multiple fully connected layers. In this work, we propose a new end-to-end MR image reconstruction technique based on the recurrent neural network (RNN) architecture, which can be more efficiently used for magnetic resonance (MR) image reconstruction than the convolutional neural network (CNN). We modified the RNN architecture of ReNet for image domain data to reconstruct an MR image from k-space data by utilizing recurrent cells. The proposed network reconstructs images from the k-space data with a reduced number of parameters compared with that of fully connected architectures. We present a quantitative evaluation of the proposed method for Cartesian trajectories using nMSE and SSIM. We also present preliminary images reconstructed from k-space data acquired in the radial trajectory.