Freezing of gait (FOG) is common in people with Parkinson’s disease (PD) which is extremely debilitating. One hypothesis for the cause of FOG episodes is impaired cognitive control, however, this is still in debate in the literature. We aimed to assess a comprehensive range of cognitive tests in older adults and people with Parkinson’s with and without FOG and associate FOG severity with cognitive performance. A total of 227 participants took part in the study which included 80 healthy older adults, 81 people with PD who did not have FOG and 66 people with PD and FOG. A comprehensive battery of neuropsychological assessments tested cognitive domains of global cognition, executive function/attention, working memory, and visuospatial function. The severity of FOG was assessed using the new FOG questionnaire and an objective FOG severity score. Cognitive performance was compared between groups using an ANCOVA adjusting for age, gender, years of education and disease severity. Correlations between cognitive performance and FOG severity were analyzed using partial correlations. Cognitive differences were observed between older adults and PD for domains of global cognition, executive function/attention, and working memory. Between those with and without FOG, there were differences for global cognition and executive function/attention, but these differences disappeared when adjusting for covariates. There were no associations between FOG severity and cognitive performance. This study identified no significant difference in cognition between those with and without FOG when adjusting for covariates, particularly disease severity. This may demonstrate that complex rehabilitation programs may be undertaken in those with FOG.