Summary: We present a new method for generating multiple-scroll attractors. By constructing a piece-wise-linear odd function as the driving-point characteristic of Chua’s diode with multiple breakpoints, and finding a recurrence formula for determining equilibrium point voltages and breakpoint voltages, we can calculate the voltages of all the equilibrium points and breakpoints, and the multiple-scroll chaotic attractors can be obtained. This method is based on Shil’nikov theorem and the cell model of chaotic attractors. The theoretical calculations are in good agreement with computer simulations and hardware experimental results. Compared with the results reported by Suykens, our method has some advantages that much more scrolls can be obtained, the scrolls are uniform in size, and a general recurrence formula for generating attractors with any number of scrolls is given. Furthermore, the observation of attractors with a maximum of 11-21 uniform scrolls obtained by hardware experiment and computer simulation, respectively, is reported for the first time.