In this paper, a new four-dimensional fractional-order chaotic system is constructed by introducing a memristor as a feedback term in a fractional-order Lorenz chaotic system. The analytical solution of the system is obtained based on the Adomian decomposition method, and the system is obtained to have an infinite set of equilibrium points. From the Lyapunov exponential spectrum and bifurcation diagram, the fractional-order system exhibits rich dynamical behaviors, such as stable state, multiplicative-period bifurcation, bifurcation mode, chaotic state, etc., under the single-parameter variations are analyzed. The system is found to have double-scroll chaotic attractor, period 1 state attractor, period 2 state attractor of different types under the variation of double parameter analyzed using Lyapunov exponential spectrograms, maximum minimum phase diagrams and time series plots. According to the spectral entropy SE and C 0 complexity map, the system is analyzed to have parameter sensitivity and complex dynamics conversion, and it is concluded that the parameter b has more significant effect on the complexity of fractional-order Lorenz memristor systems, which provides good ideas for the study of fractional-order circuit systems.