In this paper, we propose a symmetric series convolutional neural network (SS-CNN), which is a novel deep convolutional neural network (DCNN)-based super-resolution (SR) technique for ultrasound medical imaging. The proposed model comprises two parts: a feature extraction network (FEN) and an up-sampling layer. In the FEN, the low-resolution (LR) counterpart of the ultrasound image passes through a symmetric series of two different DCNNs. The low-level feature maps obtained from the subsequent layers of both DCNNs are concatenated in a feed forward manner, aiding in robust feature extraction to ensure high reconstruction quality. Subsequently, the final concatenated features serve as an input map to the latter 2D convolutional layers, where the textural information of the input image is connected via skip connections. The second part of the proposed model is a sub-pixel convolutional (SPC) layer, which up-samples the output of the FEN by multiplying it with a multi-dimensional kernel followed by a periodic shuffling operation to reconstruct a high-quality SR ultrasound image. We validate the performance of the SS-CNN with publicly available ultrasound image datasets. Experimental results show that the proposed model achieves an exquisite reconstruction performance of ultrasound image over the conventional methods in terms of peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), while providing compelling SR reconstruction time.