Abstract: For the rational Bézier curve with weights in the form of exponential function, the degeneration of the curve is presented in this paper. Firstly, the weights in the form of exponential function are converted into the form of power function and we indicate the relationship between them. Based on the toric degenerations of rational Bézier curve, the regular control curve of rational Bézier curve is defined. Finally, the geometric property of the degeneration of curve of rational Bézier curve while weights approach to infinity is presented. Experimental results verify the presented result and show the differences between it and the toric degenerations of rational Bézier curve.