Abstract: A novel method of constructing C¹ rational fractal surfaces is developed with the help of classical bi-cubic rational Hermite interpolation, which provides a unified approach to the fractal generalization of various traditional bivariate rational spline interpolation. Compared with the existing fractal interpolation, this kind of rational spline fractal interpolation has the following advantages:1) The construction of bivariate rational fractal interpolation functions(BRFIFs) described here allows us to embed shape parameters within the structure of differentiable fractal functions, so that it is more flexible and diverse than the current interpolation. 2) It can be explicitly expressed by the symmetric bases and the simple matrix form. 3) The shape of the fractal interpolation surfaces can be modified by selecting suitable parameters for the unchanged interpolating data. In order to meet the needs of practical design, a monotonicity-preserving fractal surface interpolating scheme is developed to visualize monotonic data in the view of monotone surfaces by using constraints on scaling factors and shape parameters in the description of the BRFIFs. The experimental results demonstrate that the proposed model achieved competitive performance, not only subjectively but also objectively.