Compressed sensing (CS) has been exploited for accelerating data acquisition in magnetic resonance imaging (MRI). MR images can be then reconstructed from significantly fewer measurements, i.e., drastically lower than that required by the Nyquist sampling criterion. However, the compressed sensing method usually produces images with artifacts, particularly at high reduction rates. In this paper, we propose a novel compressed sensing MRI method, called CS-NLTV that exploits curvelet sparsity (CS) and nonlocal total variation (NLTV) regularization. The curvelet transform is optimal sparsifying transform with the excellent directional sensitivity than that of wavelet transform. The NLTV, on the other hand extends the total variation regularizer to a nonlocal variant which can preserve both textures and structures and produce sharper images. We have explored a new approach of combining alternating direction method of multiplier (ADMM), adaptive weighting, and splitting variables technique to solve the formulated optimization problem. The proposed CSNLTV method is evaluated experimentally and compared to the previously reported high performance methods. Results demonstrate a significant improvement of compressed MR image reconstruction on four medical MRI datasets.