Protein arginine methyltransferase 6 (PRMT6) catalyses the asymmetric dimethylation of arginines on numerous substrate proteins within the human cell. In particular, PRMT6 methylates histone H3 arginine 2 (H3R2) which affects both gene repression and activation. However, the substrate specificity of PRMT6 has not been comprehensively analysed. Here we have systematically characterised the substrate recognition motif of PRMT6 in context of the histone H3 tail, finding that it has broad specificity and recognises the RG motif. Working with a H3 tail peptide as a template, on which we made 204 amino acid substitutions, we use targeted mass spectrometry to measure the effect on PRMT6 in vitro activity. We first show that PRMT6 methylates R2 and R8 in the H3 peptide, although H3R8 is methylated with lower efficiency and is not an in vivo PRMT6 substrate. Then, using parallel reaction monitoring (PRM) with electron transfer dissociation (ETD), we quantify the effect of 194 of these amino acid substitutions on methylation at both H3R2 and H3R8. In both cases, we find that PRMT6 is capable of tolerating essentially any amino acid substitution in the H3 peptide, but that positively charged and bulky residues are preferred near the target arginine. We show that PRMT6 prefers glycine in the position immediately following the target arginine, indicating that PRMT6 recognises the RG motif. We confirm this preference for the RG motif on another PRMT6 substrate, histone H4R3. This broad specificity, along with recognition of RG rather than RGG, is distinctive among the PRMT family and has implications for the development of drugs to selectively target PRMT6.