Spectral CT based on photon counting detectors is a promising imaging modality since it provides the possibility of both obtaining CT images from multi-energy bins with a single Xray exposure and allowing low-dose imaging. However, the image quality such as spatial resolution reconstructed from multiple energy bins is degraded because of the use of narrow energy bins in spectral CT. We propose to use deep learning methods for super-resolution reconstruction of spectral CT images. To this end, we introduce an UNet-ESPC-cascaded model and perform a patch-based training to obtain the optimal parameters of the model. Experimental results on physical phantom datasets demonstrated that our deep learning based reconstruction method can reduce the F form error between the reconstructed superresolution CT image and the ground truth, by 11.6% and 5.66% with respect to respectively bilinear-interpolation-based reconstruction and iterative back projection methods. Our method achieves best results with a patch size of 20 and a stride of 15.