One of the most prevalent symptoms of post-COVID condition is cognitive impairment, which results in a significant degree of disability and low quality of life. In studies with large sample sizes, attention, memory, and executive function were reported as long-term cognitive symptoms. This study aims to describe cognitive dysfunction in large post-COVID condition individuals, compare objective neuropsychological performance in those post-COVID condition individuals with and without cognitive complaints, and identify short cognitive exams that can differentiate individuals with post-COVID symptoms from controls. To address these aims, the Nautilus project was started in June 2021. During the first year, we collected 428 participants’ data, including 319 post-COVID and 109 healthy controls (18–65 years old) from those who underwent a comprehensive neuropsychological battery for cognitive assessment. Scores on tests assessing global cognition, learning and long-term memory, processing speed, language and executive functions were significantly worse in the post-COVID condition group than in healthy controls. Montreal Cognitive Assessment, digit symbol test, and phonetic verbal fluency were significant in the binomial logistic regression model and could effectively distinguish patients from controls with good overall sensitivity and accuracy. Neuropsychological test results did not differ between those with and without cognitive complaints. Our research suggests that patients with post-COVID conditions experience significant cognitive impairment and that routine tests like the Montreal Cognitive Assessment, digit symbol, and phonetic verbal fluency test might identify cognitive impairment. Thus, the administration of these tests would be helpful for all patients with post-COVID-19 symptoms, regardless of whether cognitive complaints are present or absent.