One novel variational Retinex algorithm for infrared image enhancement is proposed to eliminate the staircase effect and enhance details. Gaussian curvature regularization is adopted to construct the variational Retinex model, and the first-order differential term is adopted to add the detail enhancement constraint, which realizes the adaptive enhancement of detail information. In combination with the neighborhood difference operation, the curvature filter solver for variational model is introduced to achieve the optimal solution. The experimental results demonstrate that, compared with those processed by the other variational Retinex algorithms, the quantitative evaluation indexes of images processed by the proposed novel algorithm are superior. The new algorithm can eliminate the staircase effect and enhance the details and visual effect of images.