Rheological property, shear stressvs.shear rate, of cholesteryl nonanoate (CN) is measured in a temperature region including the blue phases (BPs). From the measurement of the temperature dependence, an anomalous increase in the viscosity, accompanied by a non-Newtonian flow, is observed between 363.4 K and 367.5 K. The anomalous temperature region of 4.1 K obtained from the rheological measurement is wider than the BP region of 0.8 K determined from the thermal analysis, suggesting that the BP region is enlarged under an application of the steady shear flow.