We propose a free-space density functional theory for polymer adsorption. The derivation within the framework of density functional theory leads to the splitting of the intrinsic free energy into an ideal-gas term and a residual term responsible for the intrinsic energy and the nonbonded interactions between monomers, respectively. A more reasonable treatment is adopted for the residual free energy to count for the monomer-monomer correlation underestimated by the local density approximation. An approach using propagators is proposed to calculate the single-chain partition function and the segment-density distributions, the three adsorption conformations as trains, loops, and tails are further described by propagators. Dirac's bra-ket notation used makes the derivation simpler and provides clearer physical meanings. The theoretical calculations for the adsorption of hard-sphere chains onto a nonadsorbing and an adsorbing hard wall show that the structure of the adsorption layer is strongly affected by the packing effect which has been underestimated by the previous lattice adsorption theory.