Variation in human intelligence is approximately 50% heritable, but understanding of the genes involved is limited. Several forms of genetic variation remain under-studied in relation to intelligence, one of which is copy number variation (CNV). Using single-nucleotide polymorphism (SNP) -based microarrays, we genotyped CNVs genome-wide in a birth cohort of 723 New Zealanders, and correlated them with four intelligence-related phenotypes. We found no significant association for any common CNV after false discovery correction, which is consistent with previous work. In contrast to a previous study, however, we found no effect on any cognitive measure of rare CNV burden, defined as total number of bases inserted or deleted in CNVs rarer than 5%. We discuss possible reasons for this failure to replicate, including interaction between CNV and aging in determining the effects of rare CNVs. While our results suggest that no CNV assayable by SNP chips contributes more than a very small amount to variation in human intelligence, it remains possible that common CNVs in segmental duplication arrays, which are not well covered by SNP chips, are important contributors.