Infinite lines of equilibria exist in a new memristive system when a tangent function is introduced for attractor self-reproducing. Lyapunov exponent spectra and bifurcation diagram shows that the newly proposed chaotic system exhibits intermittent chaos and hypermultistability characterized for the coexistence of infinite countable and uncountable attractors. The physical feasibility of the new memristive chaotic system is confirmed by PSpice circuit simulation. Finally, the system is applied in color image encryption, where the performance in the process is evaluated. Numerical simulation proves that the new memristive chaotic system has high security in image encryption.