Creativity is associated with finding novel, surprising, and useful solutions. We argue that creative cognitive processes, divergent thinking, abstraction, and improvisation are constructed on different novelty-based processes. The prefrontal cortex plays a role in creative ideation by providing a control mechanism. Moreover, thinking about novel solutions activates the distant or loosely connected neurons of a semantic network that involves the hippocampus. Novelty can also be interpreted as different combinations of earlier learned processes, such as the motor sequencing mechanism of the basal ganglia. In addition, the cerebellum is responsible for the precise control of movements, which is particularly important in improvisation. Our neurocomputational perspective is based on three creative processes centered on novelty seeking, subserved by the prefrontal cortex, hippocampus, cerebellum, basal ganglia, and dopamine. The algorithmic implementation of our model would enable us to describe commonalities and differences between these creative processes based on the proposed neural circuitry. Given that most previous studies have mainly provided theoretical and conceptual models of creativity, this article presents the first brain-inspired neural network model of creative cognition.