Optical coherence tomography (OCT) has been widely used in ophthalmology with its micron-resolution, depth-resolving capability in imaging bio-tissues in vivo. Recently, deep learning methods are emerging to achieve axial super-resolution (SR) in OCT, aimed to reduce the cost of broad-band light source. However, all of those deep learning methods were developed based on real-valued networks, ignoring the phase information of complex-valued OCT image which contains structural information. In this study, we proposed a complex-valued enhanced deep super-resolution network (Cv-EDSR) to obtain OCT axial super-resolution. We validated the superior performance of Cv-EDSR over the traditional EDSR on two datasets (swine esophagus and human retina), and demonstrated three benefits of Cv-EDSR: a) Cv-EDSR generated more realistic SR images, b) Cv-EDSR achieved an improved quality of SR images, c) Cv-EDSR possessed a better generalization performance.