Knowledge of toxic chemical sorption by carbon nanotubes (CNTs) is critical for environmental application of CNTs as superior sorbents and for environmental risk assessment of both CNTs and toxic chemicals. Single-solute sorption results were reported in the literature, however, they cannot be used for predicting pollutant sorption by CNTs in wastewater and natural water systems where multiple organic contaminants are present. In this study, competitive sorption of pyrene, phenanthrene, and naphthalene on a multiwalled CNT material was investigated. All isotherms in single-, bi-, and tri-solute systems were fitted well by the Dubinin-Ashtakhov (DA) model. The isotherm of a given primary solute changed from being significantly nonlinear to nearly linear when competitors were added. The observed competitive sorption depended on the relative equilibrium concentrations of both primary and cosolutes. Significant competition was observed at relatively low concentrations of primary solute and high concentrations of competitors, while competition was much weaker in the case of relatively high concentrations of primary solute and low competitor concentrations. When the relative concentration of primary solute (Ce/Cs) approached 1, competition by other solutes seemed to disappear. Sorption and competition of three polycyclic aromatic hydrocarbons (PAHs) on CNTs could not be explained with either pore-filling or partition-adsorption mechanisms. A Polanyi-based surface adsorption mechanism was proposed to interpret the observed sorption and competition.