The prevalence of dementia among South Asians across India is approximately 7.4% in those 60 years and older, yet little is known about genetic risk factors for dementia in this population. Most known risk loci for Alzheimer's disease (AD) have been identified from studies conducted in European Ancestry (EA) but are unknown in South Asians. Using whole-genome sequence data from 2680 participants from the Diagnostic Assessment of Dementia for the Longitudinal Aging Study of India (LASI-DAD), we performed a gene-based analysis of 84 genes previously associated with AD in EA. We investigated associations with the Hindi Mental State Examination (HMSE) score and factor scores for general cognitive function and five cognitive domains. For each gene, we examined missense/loss-of-function (LoF) variants and brain-specific promoter/enhancer variants, separately, both with and without incorporating additional annotation weights (e.g., deleteriousness, conservation scores) using the variant-Set Test for Association using Annotation infoRmation (STAAR). In the missense/LoF analysis without annotation weights and controlling for age, sex, state/territory, and genetic ancestry, three genes had an association with at least one measure of cognitive function (FDR q<0.1). APOE was associated with four measures of cognitive function, PICALM was associated with HMSE score, and TSPOAP1 was associated with executive function. The most strongly associated variants in each gene were rs429358 (APOE e4), rs779406084 (PICALM), and rs9913145 (TSPOAP1). rs779406084 is a rare missense mutation that is more prevalent in LASI-DAD than in EA (minor allele frequency=0.075% vs. 0.0015%); the other two are common variants. No genes in the brain-specific promoter/enhancer analysis met criteria for significance. Results with and without annotation weights were similar. Missense/LoF variants in some genes previously associated with AD in EA are associated with measures of cognitive function in South Asians from India. Analyzing genome sequence data allows identification of potential novel causal variants enriched in South Asians.