Protein arginine N-methyltransferases (PRMTs) catalyze the transfer of methyl group(s) from S-adenosyl-l-methionine (AdoMet) to the guanidine group of arginine residue in abundant eukaryotic proteins. Two major types of PRMTs have been identified in mammalian cells. Type I PRMTs catalyze the formation of asymmetric ω-N^G, N^G-dimethylarginine (ADMA), while Type II PRMTs catalyze the formation of symmetric ω-N^G, N′^G-dimethylarginine (SDMA). The two different methylation products (ADMA or SDMA) of the substrate could lead to different biological consequences. Although PRMTs have been the subject of extensive experimental investigations, the origin of the product specificity remains unclear. In this study, quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) and free energy simulations are performed to study the reaction mechanism for one of Type I PRMTs, PRMT3, and to gain insights into the energetic origin of its product specificity (ADMA). Our simulations have identified some important interactions and proton transfers involving the active site residues. These interactions and proton transfers seem to be responsible, at least in part, in making the N_η2 atom of the substrate arginine the target of the both 1st and 2nd methylations, leading to the asymmetric dimethylation product. The simulations also suggest that the methyl transfer and proton transfer appear to be somehow concerted processes and that Glu326 is likely to function as the general base during the catalysis.