Dynamic behavior of heat transfer, fluid flow, and interfaces in the vertical zone-melting (VZM) crystal growth is studied numerically. The model, which is governed by axisymmetric unsteady-state momentum and heat transfer and interface balance in the system, is solved by a robust finite-volume method. Single crystal growth of NaNO3 in a computer-controlled transparent multizone furnace is simulated as examples. The effects of gravity levels and heater temperature are considered. Multiple steady states obtained at stationary cases are used as initial conditions to illustrate the transient response and the stability of the VZM crystal growth to the pulse and step changes in thermal environments. For unstable cases, periodically oscillatory flow and growth rate occurring at intermediate values of the Rayleigh number are observed. The upper flow cells beneath the feed front seems to be responsible to the instability, and this is consistent with the observation during crystal growth experiments. For stable cases, a steady state can be achieved smoothly, and the calculated results are in good agreement with the ones from a pseudo steady-state model.