The identification of loci influenced by positive selection is a major goal of evolutionary genetics. A popular approach is to perform scans of alignments on a genome-wide scale in order to find regions evolving at accelerated rates on a particular branch of a phylogenetic tree. However, positive selection is not the only process that can lead to accelerated evolution. Notably, GC-biased gene conversion (gBGC) is a recombination-associated process that results in the biased fixation of G and C nucleotides. This process can potentially generate bursts of nucleotide substitutions within hotspots of meiotic recombination. Here, we analyse the results of a scan for positive selection on genes on branches across the primate phylogeny. We show that genes identified as targets of positive selection have a significant tendency to exhibit the genomic signature of gBGC. Using a maximum-likelihood framework, we estimate that more than 20 per cent of cases of significantly elevated non-synonymous to synonymous substitution rates ratio (d(N)/d(S)), particularly in shorter branches, could be due to gBGC. We demonstrate that in some cases, gBGC can lead to very high d(N)/d(S) (more than 2). Our results indicate that gBGC significantly affects the evolution of coding sequences in primates, often leading to patterns of evolution that can be mistaken for positive selection.