Another approach is developed for generating two-wing hyperchaotic attractor, four-wing chaotic attractor, and high periodic orbits such as period-14 from a sinusoidally driven based canonical Lorenz system. A sinusoidal function controller is introduced into a 3D autonomous Lorenz system, so that the abovementioned various hyperchaotic attractors, chaotic attractors, and high periodic orbits can be obtained, respectively, by adjusting the frequency of the sine function. In addition, an analog circuit and a digital circuit are also designed and implemented, with experimental results demonstrated. Both numerical simulations and circuit implementation together show the effectiveness of the proposed systematic methodology.