Polymeric nanoparticles have emerged as efficient carriers for anticancer drug delivery because they can improve the solubility of hydrophobic drugs and also can increase the bio-distribution of drugs throughout the bloodstream. In this work, a computational study is performed on a set of new pH-sensitive polymer–drug compounds based on an intelligent polymer called poly(β-malic acid) (PMLA). The molecular dynamics (MD) simulation is used to explore the adsorption and dynamic properties of PMLA–doxorubicin (PMLA–DOX) interaction with the graphene oxide (GOX) surface in acidic and neutral environments. The PMLA is bonded to DOX through an amide bond (PMLA-ami-DOX) and a hydrazone bond (PMLA-hz-DOX) and their adsorption behavior is compared with free DOX. Our results confirm that the polymer–drug prodrug shows unique properties. Analysis of the adsorption behavior reveals that this process is spontaneous and the most stable complex with a binding energy of −1210.262 kJ mol⁻¹ is the GOX/PMLA-hz-DOX complex at normal pH. On the other hand, this system has a great sensitivity to pH so that in an acidic environment, its interaction with GOX became weaker while such behavior is not observed for the PMLA-ami-DOX complex. The results obtained from this study provide accurate information about the interaction of the polymer–drug compounds and nanocarriers at the atomic level, which can be useful in the design of smart drug delivery systems.