Experimental studies of reasoning and planned behavior have provided evidence that nervous systems use internal models to perform predictive motor control, imagery, inference, and planning. Classical (model-free) reinforcement learning approaches omit such a model; standard sensorimotor models account for forward and backward functions of sensorimotor dependencies but do not provide a proper neural representation on which to realize planning. We propose a sensorimotor map to represent such an internal model. The map learns a state representation similar to self-organizing maps but is inherently coupled to sensor and motor signals. Motor activations modulate the lateral connection strengths and thereby induce anticipatory shifts of the activity peak on the sensorimotor map. This mechanism encodes a model of the change of stimuli depending on the current motor activities. The activation dynamics on the map are derived from neural field models. An additional dynamic process on the sensorimotor map (derived from dynamic programming) realizes planning and emits corresponding goal-directed motor sequences, for instance, to navigate through a maze.