We report the discovery of the anomalous enhancement of quantum coherent dynamics (CD) due to a non-Markovian mechanism originating from not thermal-equilibrium phonon baths but nonequilibrium coherent phonons. CD is an elementary process for quantum phenomena in nanosystems, such as excitation transfer (ET) in semiconductor nanostructures and light-harvesting systems. CD occurs in homogeneous nanosystems because system inhomogeneity typically destroys coherence. In real systems, however, nanosystems behave as open systems surrounded by environments such as phonon systems. Typically, CD in inhomogeneous nanosystems is enhanced by the absorption and emission of thermal-equilibrium phonons, and the enhancement is described by the conventional master equation. On the other hand, CD is also enhanced by synchronization between population dynamics in nanosystems and coherent phonons; namely, coherent phonons, which are self-consistently induced by phase matching with Rabi oscillation, are fed back to enhance CD. This anomalous enhancement of CD essentially originates from the nonequilibrium and dynamical non-Markovian nature of coherent phonon environments, and the enhancement is firstly predicted by applying time-dependent projection operators to nonequilibrium and dynamical environments. Moreover, CD is discussed by considering ET from a donor to an acceptor. It is found that the enhancement of ET by synchronization with coherent phonons depends on the competition between the output time from a system to an acceptor and the formation time of coherent phonons. These findings in this study will stimulate the design and manipulation of CD via structured environments from the viewpoint of application to nano-photoelectronic devices.