A constant transconductance input and output rail-to-rail fully differential amplifier with continuous time common-mode feedback is proposed. The input stage complementary difference pair uses cross conduction to keep the total input transconductance constant in the whole common-mode input range. The intermediate stage adopts folded common source and common gate structure to achieve high gain and full swing. At the same time, A continuous-time common-mode feedback circuit with A class A output structure is designed to enable FDA to work in large swing and high impedance systems. Based on SMIC 0.18 μm process, the designed FDA was simulated and verified and the layout was drawn. When the supply voltage was 3.3 V and the load capacitance was 5 pF, the DC gain of the circuit was 92.2 dB, the unit gain bandwidth was 5.55 MHz, the input-output rail-to-rail range was close to 100%, and the input-stage transconductance change rate was only 4.53%. The setup time is 218 and 195.7 ns, respectively, and the corresponding swing rate is 15 and 16.7 V/μs, respectively.