We study the time-evolutional behavior of selforganized Turing pattern under spatiotemporal forcing in one-dimensional systems. Based on the model equations, we apply a space-time dependent external force. Entrainment and modulation of time-evolutional patterns are investigated numerically in one dimension. We develop a theoretical analysis to understand the obtained dynamics. Moreover, we discuss the relationship between the behavior of time-evolutional patterns in Turing system with external force and the mode selection problem that is the fundamental unsolved problem in non-equilibrium open systems.