In this paper, bandgap reference PTAT(Proportional to Absolute Temperature) circuit and flexible gain control of LNA(Low Noise Amplifier) which is usable in Zigbee system of 2.4GHz band are designed by TSMC $0.18{mu}m$ CMOS library. PTAT bandgap reference circuit is proposed to minimize the instability of CMOS circuit which may be unstable in temperature changes. This circuit is designed such that output voltage remains within 1.3V even when the temperature varies from $-40^{circ}C$ to $-50^{circ}C$ when applied to the gate bias voltage of LNA. In addition, the LNA is designed to be operated on 2.4GHz which is applicable to Zigbee system and able to select gains by changing output impedance using 4 NMOS operated switches. The simulation result shows that achieved gain is 14.3~17.6dB and NF (Noise Figure) 1.008~1.032dB.