The microphase ordering processes for ABC linear triblock copolymers are investigated using dynamic density functional theory (DDFT). The implementation of the DDFT is verified by comparing the 2D equilibrium triblock morphologies it predicted with previous theory and experiments. Quenched from a disordered state, the microphase separation of the ABC triblock copolymers may proceed through either one-step or two-step ordering mechanism, depending on the composition and the interaction energies of the three components. When the volume fraction of one species dominates the other two, the microphase ordering always proceeds through a two-step mechanism with the majority one segregating at first, provided a three-phase morphology formed at the end. When the volume fractions of the three species are comparable, for the symmetric interaction case, the microphase separation occurs through a one-step mechanism, while for the asymmetric interaction case, it occurs through a two-step mechanism with the most incompatible species segregating at first.