Deep Convolutional Neural Networks (CNNs) have achieved remarkable results on Single Image Super-Resolution (SISR). Despite considering only a single degradation, recent studies also include multiple degrading effects to better reflect real-world cases. However, most of the works assume a fixed combination of degrading effects, or even train an individual network for different combinations. Instead, a more practical approach is to train a single network for wide-ranging and variational degradations. To fulfill this requirement, this paper proposes a unified network to accommodate the variations from inter-image (cross-image variations) and intra-image (spatial variations). Different from the existing works, we incorporate dynamic convolution which is a far more flexible alternative to handle different variations. In SISR with non-blind setting, our Unified Dynamic Convolutional Network for Variational Degradations (UDVD) is evaluated on both synthetic and real images with an extensive set of variations. The qualitative results demonstrate the effectiveness of UDVD over various existing works. Extensive experiments show that our UDVD achieves favorable or comparable performance on both synthetic and real images.