Hyperspectral (HS) image can describe subtle differences in the spectral signatures of materials, but it has low spatial resolution limited by the existing technical and budget constraints. In this paper, we propose a promising HS pansharpening method with deep priors (HPDP) to fuse a low-resolution (LR) HS image with a high-resolution (HR) panchromatic (PAN) image. Different from the existing methods, we redefine the spectral response function (SRF) based on the larger eigenvalue of structure tensor (ST) matrix for the first time that is more in line with the characteristics of HS imaging. Then, we introduce HFNet to capture deep residual mapping of high frequency across the upsampled HS image and the PAN image in a band-by-band manner. Specifically, the learned residual mapping of high frequency is injected into the structural transformed HS images, which are the extracted deep priors served as additional constraint in a Sylvester equation to estimate the final HR HS image. Comparative analyses validate that the proposed HPDP method presents the superior pansharpening performance by ensuring higher quality both in spatial and spectral domains for all types of data sets. In addition, the HFNet is trained in the high-frequency domain based on multispectral (MS) images, which overcomes the sensitivity of deep neural network (DNN) to data sets acquired by different sensors and the difficulty of insufficient training samples for HS pansharpening.