Coherent imaging systems like synthetic aperture radar are susceptible to multiplicative noise that makes applications like automatic target recognition challenging. In this paper, NeighCNN, a deep learning-based speckle reduction algorithm that handles multiplicative noise with relatively simple convolutional neural network architecture, is proposed. We have designed a loss function which is an unique combination of weighted sum of Euclidean, neighbourhood, and perceptual loss for training the deep network. Euclidean and neighbourhood losses take pixel-level information into account, whereas perceptual loss considers high-level semantic features between two images. Various synthetic, as well as real SAR images, are used for testing the NeighCNN architecture, and the results verify the noise removal and edge preservation abilities of the proposed architecture. Performance metrics like peak-signal-to-noise ratio, structural similarity index, and universal image quality index are used for evaluating the efficiency of the proposed architecture on synthetic images.