Acoustic Scene Classification (ASC) is one of the core research problems in the field of Computational Sound Scene Analysis. In this work, we present SubSpectralNet, a novel model which captures discriminative features by incorporating frequency band-level differences to model soundscapes. Using mel-spectrograms, we propose the idea of using band-wise crops of the input time-frequency representations and train a convolutional neural network (CNN) on the same. We also propose a modification in the training method for more efficient learning of the CNN models. We first give a motivation for using sub-spectrograms by giving intuitive and statistical analyses and finally we develop a sub-spectrogram based CNN architecture for ASC. The system is evaluated on the public ASC development dataset provided for the "Detection and Classification of Acoustic Scenes and Events" (DCASE) 2018 Challenge. Our best model achieves an improvement of +14% in terms of classification accuracy with respect to the DCASE 2018 baseline system. Code and figures are available at https://github.com/ssrp/SubSpectralNet