The drive beam injector for CLIC needs to deliver a 4.2 A electron beam for a duration of 140 μs with a repetition rate of 50 Hz. The shot to shot and flat top current stability has to be better than 0.1% to guarantee the beam stability required for CLIC. Based on the experience with the CTF3 injector a thermionic high voltage gun with a gridded cathode has been designed together with a sub-harmonic bunching system to achieve these requirements. The grid will allow controlling the current and eventually feedback on the flattop shape. The gun will operate at 140 kV and an emittance of 14 mm mrad can be obtained. The paper describes the design approach and the results of the systematic electromagnetic simulations to optimize the gun. Care was taken during the mechanical design of the gun to obtain a modular design allowing adjusting for different beam currents and cathode sizes.