A unified potentiostat circuit for both $O_2$- and $H_2O_2$- based electrochemical glucose sensors was proposed and its function was verified by circuit simulations and measurement results of a fabricated chip. This circuit consisted of an operational amplifier, a comparator and current mirrors. The proposed circuit was fabricated with a $0.13{mu}m$ thick oxide CMOS process and an active area of $360{mu}m{ imes}100{mu}m$. The measurements revealed an input operation range from 0.5 V to 1.6 V in the $H_2O_2$- based bio-sensor and from 1.7 V to 2.6 V in the $O_2$- based bio-sensor with a supply voltage of 3.3 V. The evaluation results showed that the proposed potentiostat circuit is suitable for measuring the electrochemical cell currents of both $O_2$- and $H_2O_2$- based glucose sensors.