Recently deep learning techniques have significantly advanced image super-resolution (SR). Due to the black-box nature, quantifying reconstruction uncertainty is crucial when employing these deep SR networks. Previous approaches for SR uncertainty estimation mostly focus on capturing pixel-wise uncertainty in the spatial domain. SR uncertainty in the frequency domain which is highly related to image SR is seldom explored. In this paper, we propose to quantify spectral Bayesian uncertainty in image SR. To achieve this, a Dual-Domain Learning (DDL) framework is first proposed. Combined with Bayesian approaches, the DDL model is able to estimate spectral uncertainty accurately, enabling a reliability assessment for high frequencies reasoning from the frequency domain perspective. Extensive experiments under non-ideal premises are conducted and demonstrate the effectiveness of the proposed spectral uncertainty. Furthermore, we propose a novel Spectral Uncertainty based Decoupled Frequency (SUDF) training scheme for perceptual SR. Experimental results show the proposed SUDF can evidently boost perceptual quality of SR results without sacrificing much pixel accuracy.