Cellulose paper has strong potential as an analytical platform owing to its unique characteristics. In the present study, we investigated a procedure for functionalizing the surface of cellulose paper by dip-coating a mixture of a functional polymer and a perfluoroalkylated surfactant (surfactant 1). The functional polymer comprised a mixture of methyl methacrylate and poly(ethylene glycol) methacrylate monomers. The monomer ratio in the functional polymer affected the hydrophilicity and water absorbance of the cellulose paper after dip-coating. Furthermore, the presence of surfactant 1 during dip-coating promoted the surface segregation of poly(ethylene glycol) (PEG) moieties in the polymer, which enhanced the hydrophilicity, prevented nonspecific protein adsorption, and maintained the water absorbance of the dip-coated cellulose paper. Dip-coating with another functional polymer containing biotin groups produced a cellulose paper with a biotin-decorated surface in a one-step procedure. The displayed biotin groups immobilized avidin on the surface, and the PEG moieties in the polymer prevented nonspecific protein adsorption. We then immobilized a thrombin-binding DNA aptamer on the avidin-immobilized cellulose paper to prepare a paper-based analytical device. It is possible to visualize thrombin in model solutions and serum using the paper-based analytical device.