Non-Markov dynamics for open systems of a microcavity coupled to a general resonator with Lorentzian form are studied. Using the exact master equation of the reduced density operator, the propagating (retarded) Green function and correlation Green function which the non-Markov dynamics are completely determined by are solved analytically. The state and dissipation dynamics of the cavity are studied by numerically solving the Green function, and the evolution of them with time under different half-widths of the spectral density and detuning is discussed. It shows that the stronger the coherence is, the longer time of the non-Markov effect becomes.