Hot-wire anemometry (HWA) is used for measuring velocity fluctuations such as turbulent flows. It is generally operated in three modes; constant-temperature (CT), constant-current (CC) and constant-voltage (CV) types. The constant-temperature anemometer (CTA) is the mainstream anemometer, while others are rarely used in measuring normal turbulent flows because of their insufficient response speed. However, since the constant-current anemometer (CCA) can be composed of simple circuits, the HWA can be realized at quite a low cost. In this study, the response characteristics of the CCA are theoretically analyzed, and a compensation scheme is proposed. The scheme is experimentally tested in a turbulent wake flow formed behind a cylinder. As a result, it has been confirmed that the root-mean-square (rms) velocities and the power-spectrum distributions compensated by the present scheme agree well with those measured with CTA. Hence, the CCA provides reliable measurement of turbulent velocity fluctuations.