The cerebellum cooperates with the neocortex in language processing, particularly during language acquisition, but little is known about the circuit computations underlying cerebellar language functions. Here, to simulate language acquisition, we created a biologically constrained cerebellar artificial neural network (cANN) model. We found that as the cANN acquired prediction of future words, a second function—syntactic recognition, the extraction of rules from word sequences—emerged spontaneously in the middle layer of the circuit. This single-circuit computation as the common basis for two language functions can be generalized to prediction and rule-extraction functions underlying a wide range of cerebellar cognitive functions, and also suggests a concrete novel rehabilitation method for patients with language dysfunction.