This article describes the mineralization behavior of CaCO3 crystals on electrospun cellulose acetate (CA) fibers by using poly(acrylic acid) (PAA) as a crystal growth modifier and further templating synthesis of CaCO3 microtubes. Calcite film coatings composed of nanoneedles can form on the surfaces of CA fibers while maintaining the fibrous and macro-porous structures if the concentration of PAA is in a suitable range. In the presence of a suitable concentration of PAA, the acidic PAA molecules will first adsorb onto the surface of CA fibers by the interaction between the OH moieties of CA and the carboxylic groups of PAA, and then the redundant carboxylic groups of PAA can ionically bind Ca2+ ions on the surfaces of CA fibers, resulting in the local supersaturation of Ca2+ ions on and near the fiber surface, which can induce the nucleation of CaCO3 on the CA fibers instead of in bulk solution. Calcite microtube networks on the macroscale can be prepared by the removal of CA fibers after the CA@CaCO3 composite is treated with acetone. When the CA fiber scaffold is immersed in CaCl2 solution with an extended incubation time, the first deposited calcite coatings can act as secondary substrate, leading to the formation of smaller calcite mesocrystal fibers. The present work proves that inorganic crystal growth can occur even at an organic interface without the need for commensurability between the lattices of the organic and inorganic counterparts.