Compressive　Sensing　for　Magnetic　Resonance　Imaging　(CS-MRI)　aims　to　reconstruct　Magnetic　Resonance　(MR)　images　from　under-sampled　raw　data.　There　are　two　challenges　to　improve　CS-MRI　methods,　i.e.　designing　an　under-sampling　algorithm　to　achieve　optimal　sampling,　as　well　as　designing　fast　and　small　deep　neural　networks　to　obtain　reconstructed　MR　images　with　superior　quality.　To　improve　the　reconstruction　quality　of　MR　images,　we　propose　a　novel　deep　convolutional　neural　network　architecture　for　CS-MRI　named　MRCSNet.　The　MRCSNet　consists　of　three　sub-networks,　a　compressive　sensing　sampling　sub-network,　an　initial　reconstruction　sub-network,　and　a　refined　reconstruction　sub-network.　Experimental　results　demonstrate　that　MRCSNet　generates　high-quality　reconstructed　MR　images　at　various　under-sampling　ratios,　and　also　meets　the　requirements　of　real-time　CS-MRI　applications.　Compared　to　state-of-the-art　CS-MRI　approaches,　MRCSNet　offers　a　significant　improvement　in　reconstruction　accuracies,　such　as　Peak　Signal-to-Noise　Ratio　(PSNR)　and　Structural　Similarity　(SSIM).　Besides,　it　reduces　the　reconstruction　error　evaluated　by　the　Normalized　Root-Mean-Square　Error　(NRMSE).　The　source　codes　are　available　at　https://github.com/TaihuLight/MRCSNet.　©　2021　World　Scientific　Publishing　Company.