A positive relationship between brain volume and intelligence has been suspected since the 19th century, and empirical studies seem to support this hypothesis. However, this claim is controversial because of concerns about publication bias and the lack of systematic control for critical confounding factors (e.g., height, population structure). We conducted a preregistered study of the relationship between brain volume and cognitive performance using a new sample of adults from the United Kingdom that is about 70% larger than the combined samples of all previous investigations on this subject ( N = 13,608). Our analyses systematically controlled for sex, age, height, socioeconomic status, and population structure, and our analyses were free of publication bias. We found a robust association between total brain volume and fluid intelligence ( r = .19), which is consistent with previous findings in the literature after controlling for measurement quality of intelligence in our data. We also found a positive relationship between total brain volume and educational attainment ( r = .12). These relationships were mainly driven by gray matter (rather than white matter or fluid volume), and effect sizes were similar for both sexes and across age groups.