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Compressed sensing based magnetic resonance imaging (CS-MRI) provides an efficient way to reduce scanning time of MRI. Recently deep learning has been introduced into CS-MRI to further improve the image quality and shorten reconstruction time. In this paper, we propose an efficient structurally strengthened Generative Adversarial Network, termed ESSGAN, for reconstructing MR images from highly under-sampled k-space data. ESSGAN consists of a structurally strengthened generator (SG) and a discriminator. In SG, we introduce strengthened connections (SCs) to improve the utilization of the feature maps between the proposed strengthened convolutional autoencoders (SCAEs), where each SCAE is a variant of a typical convolutional autoencoder. In addition, we creatively introduce a residual in residual block (RIRB) to SG. RIRB increases the depth of SG, thus enhances feature expression ability of SG. Moreover, it can give the encoder blocks and the decoder blocks richer texture features. To further reduce artifacts and preserve more image details, we introduce an enhanced structural loss to SG. ESSGAN can provide higher image quality with less model parameters than the state-of-the-art deep learning-based methods at different undersampling rates of different subsampling masks, and reconstruct a 256*256 MR image in tens of milliseconds., Comment: 28 pages