This paper studies the effect of the eccentricity between the inner bob and theouter cup in a coaxial viscometer on the measurements of the viscosity by using aperturbation scheme, Our numerical examples demonstrate that the error incurred bythe eccentricity would become larger as the characteristic Reynolds number decreasesor as the gap width between the bob and the cup gets narrower. However, such errorsmay not be signifcant if the eccentric distance is not larger than 1/10 of the gapwidth for the usual working range of a coaxial viscometer.