In this paper, a new scheme for single image super resolution using convolutional neural networks and subband reconstruction theory is proposed. In the design of the network, which is referred to as SRSubBandNet, each subband of the residual signal between the high and low resolution images is reconstructed from all the previous subbands. Skip connections between the first, middle and the last SRBs are utilized to address the gradient vanishing problem in the proposed network. SRSubBandNet provides competitive results in terms of both subjective and objective qualities when applied to various benchmark datasets.