Cognitive function such as reasoning, attention, memory, and language is strongly correlated with brain aging. Compared to non-Hispanic whites, Hispanics/Latinos have a higher risk of cognitive impairment and dementia. The genetic determinants of cognitive function have not been widely explored in this diverse and admixed population. We conducted a genome-wide association analysis of cognitive function in up to 7600 middle aged and older Hispanics/Latinos (mean = 55 years) from the Hispanic Community Health Study / Study of Latinos (HCHS/SOL). Four cognitive measures were examined: the Brief Spanish English Verbal Learning Test (B-SEVLT), the Word Fluency Test (WFT), the Digit Symbol Substitution Test (DSST), the Six-Item Screener (SIS). Four novel loci were identified: one for B-SEVLT at 4p14, two for WFT at 3p14.1 and 6p21.32, and one for DSST at 10p13. These loci implicate genes highly expressed in brain and previously connected to neurological diseases (UBE2K, FRMD4B, the HLA gene complex). By applying tissue-specific gene expression prediction models to our genotype data, additional genes highly expressed in brain showed suggestive associations with cognitive measures possibly indicating novel biological mechanisms, including IFT122 in the hippocampus for SIS, SNX31 in the basal ganglia for B-SEVLT, RPS6KB2 in the frontal cortex for WFT, and CSPG5 in the hypothalamus for DSST. These findings provide new information about the genetic determinants of cognitive function in this unique population. In addition, we derived a measure of general cognitive function based on these cognitive tests and generated genome-wide association summary results, providing a resource to the research community for comparison, replication, and meta-analysis in future genetic studies in Hispanics/Latinos.