The phenomena of reduced viscosity bending up and sometimes appearing a maximum in extremely dilute concentration regime of polymer solution are resulted from the concentration reduction due to adsorption of polymer onto the glass capillary wall. A quantitative theoretical description of this effect based on Langmuir adsorption isotherm is given. Applying the deduced formula to fit Ohrn’s precisely measured reduced viscosity data of polystyrene, linear and branched polyvinyl acetate solutions for three viscometers with different capillary radius gave satisfactory results. The radius dependence of the effective adsorption layer thickness of these polymers indicates it consists of two parts, that is a true adsorption layer and a repulsion layer between anchored chains on the capillary surface and flowing chains in solution. The reduced viscosities of an ultrahigh molar mass polyethylene oxide sample in aqueous solution were measured both by an ordinary glass viscometer and by a viscometer constructed with a polytetrafluoroethylene capillary. The former exhibits a maximum due to adsorption and the later possesses the typical behavior of slipping flow. After correction for solute adsorption and slippage, respectively, the two sets of data coincide well and gave a common linear reduced viscosity plot down to extremely dilute concentration regime.