By introducing three parameters to the basic Sprott-I system, an extension Sprott-I system is proposed in this paper. The system has one unstable equilibrium point, from which a single-scroll chaotic attractor can be evolved. The dynamic analysis for the system is carried out by the numerical simulation of Lyapunov exponent spectrum and bifurcation diagram to different parameters. The results show that the change to one of the parameters can lead the system to chaos by inverse period-doubling bifurcation, but the other two parameters can keep constant Lyapunov exponent spectrum. Further theoretical analysis indicates that the two parameters also have the characteristic of global amplitude modulation and the control function of phase inversion. Moreover, with discretization to the system by improved Euler algorithm, the correlative experimental verification is performed through microcontroller MSP430F249, thereby the feasibility of the discretization implementation to the system is proved.