By introducing linear terms and constant terms in dynamic equations, the extension system with constant Lyapunov exponent spectrum is proposed based on the improved constant-Lyapunov-exponent-spectrum system. Firstly, the dynamical behaviour of the extension system is investigated and expounded by simulation of Lyapunov exponent spectrum, bifurcation diagram and numerical analysis on amplitude evolvement of state variables. Secondly, a class of subsystems with the same properties but different phase trajectories is obtained through different combinations of linear terms from the extension system. The dynamical characteristics including equilibrium, eigenvalue and Lyapunov exponents are analyzed in detail simultaneously. Finally, it is pointed out that the chaotic system will have a tremendous application prospect in chaotic radar, secure communications and other information processing systems.