Using first-principles calculations we propose new anode materials for calcium-ion batteries, namely anthracene (AN), tetracene (TN) and pentacene (PN) crystals. We show that adsorption of calcium atoms on isolated AN, TN and PN molecules is energetically favorable, as well as intercalation into bulk crystals in a wide range of calcium concentrations. For all crystals, volume expansion during intercalation is less than 20% and for pentacene, it is less than 8%. We assess the diffusion and electronic properties of AN, TN and PN. We show that calcium diffusion barriers along the polyacene molecules are less than 0.45 eV, but calcium diffusion is limited by “jumps” between the molecules. Sequential band filling upon increasing levels of intercalation leads to the reentrant semiconducting-metallic-semiconducting behavior. Our results point to the promise of anthracene, tetracene, and pentacene as anodes for calcium-ion batteries.