Theories of the processes involved in creative cognition posit that cognitive control has a negative effect on creative idea generation but a positive effect on creative idea evaluation. Brain stimulation research has started to examine empirically the effects of cognitive control, with several reports of decreased cognitive control facilitating creative ideation. Such studies have shown how decreased cognitive control mechanisms facilitate creative idea generation, potentially by allowing participants access to less inhibited weaker-related associations, thereby increasing novelty. In the current study, we advance this line of work by investigating how cognitive control affects creative thinking, potentially inhibiting or facilitating novel idea generation based on task demands. Participants read sentences with the final word missing and were instructed to complete the sentence with an uncommon (but appropriate) ending. Participants performed this task while undergoing either anodal (excitatory), cathodal (inhibitory), or sham (control) transcranial direct current stimulation over their left prefrontal cortex. These responses were then rated for their novelty and appropriateness by an independent sample of raters. We found that anodal stimulation increased the appropriateness and decreased the novelty of participants’ responses. Contrary to previous studies, we did not find that cathodal stimulation increased the novelty of participants’ responses, which may be due to the nature of our task. Overall, we demonstrate how cognitive control mechanisms may inhibit novel idea generation.