Cognitive functioning evolves throughout life. Regular practice of stimulating activities maintains or even strengthens cognitive skills. This study investigated the effects of a cognitive training program based on complex closed-ended problem solving on innovative thinking. To this end, using partial least squares variance-based structural equation modeling, we first evaluated in 83 healthy adults how inhibition, cognitive flexibility, and reasoning were related to the distinct dimensions of innovative thinking. Second, we assessed how these interactions were modified after cognitive training based on problem solving in a subgroup of 16 subjects compared to leisure activity based on crossword solving in another subgroup of 15 subjects. Third, in a pilot fMRI study, we evaluated changes in brain connectivity at rest as a result of training in the problem solving group. Data on cognitive measures showed that innovative thinking was influenced by reasoning in control subjects, whereas it was influenced by cognitive flexibility following problem-solving training. These findings highlight that a cognitive intervention based on complex closed-ended problem solving promotes innovative thinking by changing the way subjects recruit and use relevant cognitive processes. Modifications in the restingstate connectivity of attention, default mode and visual networks were observed in the problem solving group.