Existing methods for spectral reconstruction usually learn a discrete mapping from RGB images to a number of spectral bands. However, this modeling strategy ignores the continuous nature of spectral signature. In this paper, we propose Neural Spectral Reconstruction (NeSR) to lift this limitation, by introducing a novel continuous spectral representation. To this end, we embrace the concept of implicit function and implement a parameterized embodiment with a neural network. Specifically, we first adopt a backbone network to extract spatial features of RGB inputs. Based on it, we devise Spectral Profile Interpolation (SPI) module and Neural Attention Mapping (NAM) module to enrich deep features, where the spatial-spectral correlation is involved for a better representation. Then, we view the number of sampled spectral bands as the coordinate of continuous implicit function, so as to learn the projection from deep features to spectral intensities. Extensive experiments demonstrate the distinct advantage of NeSR in reconstruction accuracy over baseline methods. Moreover, NeSR extends the flexibility of spectral reconstruction by enabling an arbitrary number of spectral bands as the target output.