A simple memristor-based chaotic circuit with an active flux-controlled memristor characterized by a smooth continuous cubic nonlinearity is designed. The proposed chaotic circuit can generate a 2-scroll chaotic attractor on a finite time scale and has an equilibrium set with its stability dependent on the initial state of the memristor. The complex dynamics of the proposed chaotic circuit under different initial state of the memristor are investigated both theoretically and numerically. In particular, some novel transient transition behaviors with different time scales are found in the memristor circuit. Experimental observations based on a universal circuit implementation platform are conducted to partially verify the numerical simulation results.