Dual methyltransferase that catalyzes methylation of elongation factor 1-alpha (EEF1A1 and EEF1A2 at two different positions, and is therefore involved in the regulation of mRNA translation. Via its C-terminus, methylates EEF1A1 and EEF1A2 at the N-terminal residue 'Gly-2'. Via its N-terminus dimethylates EEF1A1 and EEF1A2 at residue 'Lys-55'. Has no activity towards core histones H2A, H2B, H3 and H4. Negatively regulates cell proliferation at G1/S transition via transcriptional suppression of cell cycle regulatory genes such as CDK4 and CDK6.