The cerebellum, interconnected with the cerebral neocortex, plays a vital role in human-characteristic cognition such as language processing, however, knowledge about the underlying circuit computation of the cerebellum remains very limited. To gain a better understanding of the computation underlying cerebellar language processing, we developed a biologically constrained cerebellar artificial neural network (cANN) model, which implements the recently identified cerebello-cerebellar recurrent pathway. We found that while cANN acquires prediction of future words, another function of syntactic recognition emerges in the middle layer of the prediction circuit. The recurrent pathway of the cANN was essential for the two language functions, whereas cANN variants with further biological constraints preserved these functions. Considering the uniform structure of cerebellar circuitry across all functional domains, the single-circuit computation, which is the common basis of the two language functions, can be generalized to fundamental cerebellar functions of prediction and grammar-like rule extraction from sequences, that underpin a wide range of cerebellar motor and cognitive functions. This is a pioneering study to understand the circuit computation of human-characteristic cognition using biologically-constrained ANNs.