In recent years, there has been a growing interest in applying convolutional neural networks (CNNs) to low-level vision tasks such as denoising and super-resolution. Due to the coherent nature of the image formation process, the optical coherence tomography (OCT) images are inevitably affected by noise. This paper proposes a new method named the multi-input fully-convolutional networks (MIFCN) for denoising of OCT images. In contrast to recently proposed natural image denoising CNNs, the proposed architecture allows the exploitation of high degrees of correlation and complementary information among neighboring OCT images through pixel by pixel fusion of multiple FCNs. The parameters of the proposed multi-input architecture are learned by considering the consistency between the overall output and the contribution of each input image. The proposed MIFCN method is compared with the state-of-the-art denoising methods adopted on OCT images of normal and age-related macular degeneration eyes in a quantitative and qualitative manner.