Summary: Seismic data denoising is a basic issue of seismic data processing, and its signal-to-noise ratio affects directly the reliability of seismic data and the accuracy of geological interpretation. In this paper, we firstly construct an edge detection function based on a nonlinear diffusion. On the basis, we establish a fractional adaptive edge-preserving denoising model in the variational framework, and calculate the fractional Euler-Lagrange equation for solving the proposed model. Finally, the proposed method is applied to synthetic seismic data and field seismic data denoising, and the effectiveness and practicability of the new method are verified by comparing with the traditional denoising method.