Spectral super-resolution (SSR) aims at generating a hyperspectral image (HSI) from a given RGB image. Recently, a promising direction is to learn a complicated mapping function from the RGB image to the HSI counterpart using a deep convolutional neural network. This essentially involves mapping the RGB context within a size-specific receptive field centered at each pixel to its spectrum in the HSI. The focus thereon is to appropriately determine the receptive field size and establish the mapping function from RGB context to the corresponding spectrum. Due to their differences in category or spatial position, pixels in HSIs often require different-sized receptive fields and distinct mapping functions. However, few efforts have been invested to explicitly exploit this prior.To address this problem, we propose a pixel-aware deep function-mixture network for SSR, which is composed of a new class of modules, termed function-mixture (FM) blocks. Each FM block is equipped with some basis functions, i.e., parallel subnets of different-sized receptive fields. Besides, it incorporates an extra subnet as a mixing function to generate pixel-wise weights, and then linearly mixes the outputs of all basis functions with those generated weights. This enables us to pixel-wisely determine the receptive field size and the mapping function. Moreover, we stack several such FM blocks to further increase the flexibility of the network in learning the pixel-wise mapping. To encourage feature reuse, intermediate features generated by the FM blocks are fused in late stage, which proves to be effective for boosting the SSR performance. Experimental results on three benchmark HSI datasets demonstrate the superiority of the proposed method.