Molecular dynamics (MD) simulations were performed to investigate the influence of curvature and backbone rigidity of an oxygenated surface, here graphene oxide (GO), on its adsorption of uranyl in collaboration with humic acid (HA). The planar curvature of GO was found to be beneficial in impeding the folding of HA. This, together with its rigidity that helps stabilize the extended conformation of HA, offered rich binding sites to interact with uranyl with only marginal loss of binding strength. According to our simulations, the interaction between uranyl and GO was mainly driven by electrostatic interactions. The presence of HA not only provided multiple sites to compete/cooperate with GO for adsorption of free uranyl but also interacted with GO acting as a "bridge" to connect uranyl and GO. The potential of mean force (PMF) profiles implied that HA significantly enhanced the interaction strength between uranyl and GO and stabilized the uranyl-GO complex. Meanwhile, GO could reduce the diffusion coefficients of uranyl and HA and retard their migrations in aqueous solution. This work provides theoretical hints on the GO-based remediation strategies for the sites contaminated by uranium or other heavy metal ions and oxygenated organic pollutants.