In this brief, a novel three-dimensional non-autonomous chaotic system with periodic excitation and trigonometric function is proposed. Interestingly, with the disturbance of the periodic excitation, the system exhibits complex dynamical behaviors, including bursting oscillations (BOs), chaotic and hyperchaotic attractor. More importantly, because of the presence of trigonometric function, the system possesses infinite number of equilibrium points, which leads to the phenomenon of extreme multistability, namely infinite coexistence attractors and BOs. Besides, a variety of dynamic analysis tools such as phase diagram (PD), transformed phase diagram (TPD), time series (TS), bifurcation diagram (BD) and Lyapunov exponents (LE) are used to comprehensively analyze these interesting dynamics. Finally, an analog circuit is designed through the use of circuit simulation software PSPICE and realized by an experimental set-up to verify these dynamics.