This study employs density functional theory (DFT) to investigate the interaction between methotrexate (MTX) and glycine-conjugated poly(lactic-co-glycolic acid) (Gly-PLGA). Using optimization based on machine learning algorithms, the most stable configuration of states is determined, and electronic, optical, and infrared (IR) vibrational spectra are calculated. This research aims to explore whether Gly-PLGA can carry MTX in a chemical interaction. The results show the interaction between MTX and Gly-PLGA via hydrogen bonding at binding energies of −0.974 eV (complex A) and −0.891 eV (complex B), indicating that Gly-PLGA can indeed carry MTX through chemical interaction. The sample density of state (DOS) reveals that MTX affects the HOMO and LUMO levels, and there is a charge transfer of +0.82 |e| to the Gly-PLGA structure. The optical absorption diagram of stable optimal states confirms the existence of main peaks in the range of 250 to 300 nm, consistent with the reported experiments. The calculated IR spectrum is also in agreement with the measured values. Overall, these results provide valuable insights into the interaction between MTX and Gly-PLGA and could be useful for the development of drug delivery systems.