A role for the cerebellum in cognition is controversial, but it is a view that is becoming increasingly popular. The aim of the current study was to investigate this issue using transcranial Direct Current Stimulation (tDCS) during two cognitive tasks that require comparable motor skills, but different levels of working memory and attention. Three groups of twenty-two participants each performed the Paced Auditory Serial Addition Task (PASAT) and a novel variant of this task called the Paced Auditory Serial Subtraction Task (PASST), together with a verb generation task and its two controls, before and after the modulation of cortico-cerebellar connectivity using anodal or cathodal tDCS over the cerebellum. Participants' performance in the difficult PASST task significantly improved after cathodal stimulation compared to sham or anodal stimulation. Improvement in the easier PASAT was equal across all three stimulation conditions. Improvement in verbal response latencies were also greatest during the PASST task after cathodal stimulation, compared to sham and anodal stimulation, and became less variable. Results for the verb generation task complimented those for the PASST, such that the rate and consistency of participants' verbal responses were facilitated by cathodal stimulation, compared to sham and anodal stimulation. These findings suggest that DC stimulation over the right cerebellum affects working memory and attention differently depending on task difficulty. They support a role for the cerebellum in cognitive aspects of behaviour, whereby activity in the prefrontal cortex is likely dis-inhibited by cathodal tDCS stimulation over the right cerebellar cortex, which normally exerts an overall inhibitory tone on the cerebral cortex. We speculate that the cerebellum is capable of releasing cognitive resources by dis-inhibition of prefrontal regions of cerebral cortex, enhancing performance when tasks become demanding.