As for the discharge uniformity and impedance matching problems during multi-group electrode discharge at 3 kW high-power radio frequency (RF) slab CO2 lasers, the multi-group electrode discharge model is built with the Maxwell time domain difference method and the shunt inductor value is gained under the optimum discharge uniformity efficiency. The impedance of total load in the discharge electrode is calculated with the combination of the shunt inductor value and the equivalent impedance of discharge area. The impedance matching network parameters are given with the Smith circle and the impedance of total load, and the sum of impedance of total load and matched network impedance is 50 Ω which makes the RF input power completely fed. The actual measured standing wave ratio (SWR) is 1.18 when the discharge uniformity and impedance matching are satisfied simultaneously. The results show that, with the matched shunt inductors added in the time domain difference method, the fluctuation of the overall discharge uniformity of electrode slab decreases from previous 15% to 2.8% and the discharge uniformity difference between each electrode group is within 0.3%. The discharge experiment shows that, under the discharge uniformity and impedance matching conditions, the laser output power of 3.1 kW within 2 h can be stable with the fluctuation within ±1%.