Single-image super-resolution (SISR) refers to reconstructing a high-resolution image from given low-resolution observation. Recently, convolutional neural network (CNN)-based SISR methods have achieved remarkable results in terms of peak-signal-to-noise ratio and structural similarity measures. These models use pixel-wise loss functions to optimize their models, which results in blurry images. However, the generative adversarial network (GAN) has the ability to generate visually plausible solutions. The different GAN-based SISR methods obtain perceptually better SR results when compared to that with the existing CNN-based methods. However, the existing GAN-based SISR methods need a large number of training parameters in the architecture to obtain better SR performance, which makes them unsuitable for many real-world applications. We propose a computationally efficient enhanced progressive approach for SISR task using GAN, which we referred as E-ProSRGAN. In the proposed method, we introduce a novel design of residual block called enhanced parallel densely connected residual network, which helps to obtain better SR performance with less number of training parameters. The quantitative performance of the proposed E-ProSRNet (i.e., generator network of E-ProSRGAN) model is better for higher upscaling factors ×3 and ×4 for most of datasets when compared to the same obtained using different CNN-based methods whose trainable parameters are less than 7 M. In the case of upscaling factor ×2, E-ProSRNet obtains second highest structural similarity index measure values for Set5 and BSD100 datasets. The proposed E-ProSRGAN model generates SR samples with better high-frequency details and perception measures than that of the other existing GAN-based SISR methods with significant reduction in the number of training parameters for larger upscaling factor.