In an ideal current sensor, there is no power loss, giving the sensor a high level of integration and improving its efficiency. In order to achieve this for a current sensor based on the shunt resistor method, it is desirable to reduce the ohmic resistance of the shunt resistor. The resulting small voltage drop is difficult to amplify due to the inherent input offset voltage of the amplifier, which is significant compared with the maximum voltage drop across the shunt. Moreover, the input offset voltage of the amplifier varies with the temperature drift of the amplifier. In this paper we introduce a simple and inexpensive amplifier circuit that is able to amplify such small voltages by adding an artificial offset voltage to the shunt voltage. The temperature drift on the amplifier circuit will also be discussed in detail.