(1) Background: A previous study has shown that cognitive training with neurofeedback (CT-NF) using down-regulation improves cognitive functions in young adults. Neurofeedback has two strategies for manipulating brain activity (down-regulation and upregulation). However, the benefit of CT-NF with the upregulation of cognitive functions is still unknown. In this study, we investigated whether the upregulation of CT-NF improves a wide range of cognitive functions compared to cognitive training alone. (2) Methods: In this double-blinded randomized control trial (RCT), 60 young adults were randomly assigned to one of three groups: CT-NF group, CT alone group, and an active control (ACT) group who played a puzzle game. Participants in the three groups used the same device (tablet PC and 2ch NIRS (near-infrared spectroscopy)) and performed the training game for 20 min every day for four weeks. We measured brain activity during training in all groups, but only CT-NFs received NF. We also measured a wide range of cognitive functions before and after the intervention period. (3) Results: The CT-NF groups showed superior beneficial effects on episodic memory, working memory, and attention compared to the CT alone and ACT groups. In addition, the CT-NF group showed an increase in brain activity during CT, which was associated with improvements in cognitive function. (4) Discussion: This study first demonstrated that the CT-NF using the upregulation strategy has beneficial effects on cognitive functions compared to the CT alone. Our results suggest that greater brain activities during CT would enhance a benefit from CT.