It is well known that Bézier curve and rational Bézier curve play a very important role in the field of Computer Aided Geometric Design &Computer Graphics. They can be used to generate different curves in given condition. So far

some problems can' t be well solved in the regulation of weight factor selecting and the algorithm complexity of curve design. Based on Bernstein polynomials

a new kind of function-Bernstein Function Class is constructed in this paper. Its correlative properties are deduced in details. At the same time

the generating method of Bézier curve class is given. It can be concluded that Bernstein polynomials is a special member of Bernstein function class and the same relation exists between Bézier curve and Bézier curve class. In this article

RB function is chiefly introduced and the method of curve representation based on it is reasoned either. The relation between weighted RB curve and rational Bézier curve is also discussed. It is not difficult to find that weighted RB curve can partly supply the gap of traditional rational Bézier curve in weight factor selecting. So the flexibility of curve design is improved. In the end

some available conclusions and visual consequences are obtained.