Abstract: By improving the classical Lü system and introducing a generalized memristor, a novel memristor-based modified Lü system is proposed. The most important feature of this memristive system is that there does not exist any equilibrium point, thereby leading to that the forming dynamical behaviors are all hidden. By utilizing theoretical analyses and nonlinear system analysis methods of Lyapunov exponent spectrum and bifurcation diagram, the complex hidden dynamical behaviors, such as period, quasi-period, chaos, hyperchaos, and so on, with the variation of memristor gain for the memristive system are studied. In addition, when different initial conditions are used, the memristive system exhibits coexisting multiple attractors' phenomena of three different limit cycles as well as chaotic attractor and limit cycle. The hardware circuit is made and the experimental results verify the theoretical analysis and numerical simulations, and demonstrate that the proposed memristive Lü system has very abundant and complex hidden dynamical characteristics.