Cognitive impairment in older adults is a major public concern for Kazakhstan’s aging population. We aimed to (1) administer a neuropsychological test battery (NTB) in domains relevant to aging-associated cognitive impairment in a sample of adults aged 60+ without dementia in Almaty, Kazakhstan; (2) investigate the associations between demographic factors and test performance; and (3) provide information on the distribution of NTB scores as preliminary local normative data relevant for this population. A cross-sectional evaluation of 276 participants aged 60+ in Almaty, Kazakhstan, was conducted using cognitive instruments including tests of memory, attention, language, executive functions, visuospatial abilities, and processing speed. Multiple linear regression analyses were used to examine the association of demographic factors with neuropsychological test performance. The results from the regression analysis showed that those who are younger, have more years of education, are women, and are of Russian ethnicity had significantly better performance. The current study illustrated (1) the feasibility of administering the NTB to older adults in the general population in Kazakhstan; (2) the preliminary local normative neuropsychological measures; and (3) their independent associations with age, education, gender, and ethnicity. The findings are a platform for future research on dementia and cognitive impairment in older adults in Kazakhstan.