Aimed at the problem of chatter prediction of turning processing, modeling and solving of turning chatter vibration reliability were studied while the structural parameters are of stochastic behavior in the processing system. The single degree of freedom (1DOF) dynamical model of turning processing system was built, and stochastic stability lobes diagram (SLD) model of its turning chatter vibration was proposed. Monte Carlo method was adopted to solving the reliability. A CJ0625 lathe was measured to obtain the frequency response function (FRF), and the FRF and SLD diagram of the lathe system with uncertainty parameters was given. For seting of 16 pairs of parameters of cutting width and spindle speed, the reliability is calculated, which results are compared with that of analysis according to the stochastic SLD determined method.