Background: Obstructive sleep apnea increases (OSA) cognitive impairment risk. The objective of this study was to determine the impact of continuous positive airway pressure (CPAP) adherence on global cognition using the Montreal Cognitive Assessment questionnaire (MoCA). Materials and Methods: Thirty-four new patients diagnosed with moderate or severe OSA (apnea-hypopnea index AHI ≥ 15 events/h) from the CPAP group were compared with thirty-one moderate to severe OSA patients from the no-CPAP group. In addition, all patients completed the MoCA test, a patient health questionnaire (PHQ-9) for depressive symptoms, and a generalized anxiety questionnaire (GAD-7) for anxiety symptoms, at baseline, after 6 months, and after 1 year. Results: At baseline, there were no significant differences between the two groups regarding total MoCA scores, 20.9 ± 3.5 CPAP group to 19.7 ± 2.9 no-CPAP group (p = 0.159), PHQ-9 (p = 0.651), and GAD-7 (p = 0.691). After one year, improvement was observed for a total MoCA score of 22.7 ± 3.5 (p < 0.001) for the CPAP group, and significant variance of score between groups was more accentuated for delayed recall and attention (p < 0.001) sub-topic. Moreover, PHQ-9, GAD-7 scores, and the Epworth Sleepiness Scale (ESS) decreased significantly (p < 0.001) after CPAP therapy. The MoCA score was significantly correlated with years of education (r = 0.74, p < 0.001) and had a negative correlation with body mass index (BMI) (r = −0.34), ESS (r = −0.30) and PHQ-9 (r = −0.34). Conclusions: One year of CPAP adherence improved global cognition associated with OSA.