The aim of this study was to determine the neurocognitive and neuropsychiatric effects of continuous positive airway pressure treatment on patients with obstructive sleep apnea. This cross‐sectional, prospective, observational study included 126 patients with sleep apnea. The following tests were performed: the Montreal Cognitive Assessment for the evaluation of cognitive impairment, the Beck Depression Inventory, and the State‐Trait Anxiety Inventory, together with the Epworth Sleepiness Scale for the evaluation of neuropsychiatric symptoms and a person's general level of daytime sleepiness. The first measurement did not show neurocognitive impairment or a higher level of depressive and anxiety symptoms in 126 patients with obstructive sleep apnea in comparison to normative standards. After the 3‐month treatment indicated for 43 patients with obstructive sleep apnea, we did not find any significant improvement in cognitive performance (p = .213). However, patients with sleep apnea with continuous positive airway pressure treatment did show significantly less daytime sleepiness, anxiety and depressive symptoms (all p < .001). In conclusion, short‐term (3 months) treatment of patients with obstructive sleep apnea can substantially alleviate their daytime sleepiness, as well as depressive and anxiety symptoms.