Sentence processing takes place in real-time. Previous words in the sentence can influence the processing of the current word in the timescale of hundreds of milliseconds. Recent neurophysiological studies in humans suggest that the fronto-striatal system (frontal cortex, and striatum – the major input locus of the basal ganglia) plays a crucial role in this process. The current research provides a possible explanation of how certain aspects of this real-time processing can occur, based on the dynamics of recurrent cortical networks, and plasticity in the cortico-striatal system. We simulate prefrontal area BA47 as a recurrent network that receives on-line input about word categories during sentence processing, with plastic connections between cortex and striatum. We exploit the homology between the cortico-striatal system and reservoir computing, where recurrent frontal cortical networks are the reservoir, and plastic cortico-striatal synapses are the readout. The system is trained on sentence-meaning pairs, where meaning is coded as activation in the striatum corresponding to the roles that different nouns and verbs play in the sentences. The model learns an extended set of grammatical constructions, and demonstrates the ability to generalize to novel constructions. It demonstrates how early in the sentence, a parallel set of predictions are made concerning the meaning, which are then confirmed or updated as the processing of the input sentence proceeds. It demonstrates how on-line responses to words are influenced by previous words in the sentence, and by previous sentences in the discourse, providing new insight into the neurophysiology of the P600 ERP scalp response to grammatical complexity. This demonstrates that a recurrent neural network can decode grammatical structure from sentences in real-time in order to generate a predictive representation of the meaning of the sentences. This can provide insight into the underlying mechanisms of human cortico-striatal function in sentence processing.