We propose a high-speed and accurate hybrid dynamic density functional theory for the computer simulations of the phase separation processes of polymer melts and blends. The proposed theory is a combination of the dynamic self-consistent-field (SCF) theory and a time-dependent Ginzburg-Landau type theory with the random phase approximation (GRPA). The SCF theory is known to be accurate in evaluating the free energy of the polymer systems in both weak and strong segregation regions although it has a disadvantage of the requirement of a considerable amount of computational cost. On the other hand, the GRPA theory has an advantage of much smaller amount of required computational cost than the SCF theory while its applicability is limited to the weak segregation region. To make the accuracy of the SCF theory and the high-performance of the GRPA theory compatible, we adjust the chemical potential of the GRPA theory by using the SCF theory every constant time steps in the dynamic simulations. The performance of the GRPA and the hybrid theories is tested by using several systems composed of an A/B homopolymer, an AB diblock copolymer, or an ABC triblock copolymer. Using the hybrid theory, we succeeded in reproducing the metastable complex phase-separated domain structures of an ABC triblock copolymer observed by experiments.