Metal organic frameworks (MOFs) have been recognized as promising materials for biomedical applications such as drug storage and drug delivery. In this study, grand canonical Monte Carlo simulations were carried out to investigate the adsorption of an antihypertensive drug amlodipine in 28 different MOFs. Among them, 19 MOFs, which were identified to outperform those traditional materials, were screened to perform molecular dynamic (MD) simulations in order to select promising candidates for drug carriers of amlodipine, and then five representative MOFs were explored further to elucidate the mechanism of amlodipine adsorption. This is the first study to investigate the correlations between self-diffusion coefficients of drug molecule and its adsorption heat, pore volumes, and largest cavity diameters of MOF-74 series. This work provides valuable insights in drug adsorption and diffusion mechanisms in MOFs at the molecular level enabling us to speed up the MD screening of suitable drug carriers prior to experiments.