We present a conceptual design for an L-band (1.3 GHz) rf gun with a two-grid thermionic cathode assembly. The rf gun is designed to provide a 9 mA average beam current for 1 ms pulses at a 5 Hz rate. These parameters match the beam requirements for both the ILC and the Fermilab Project X test facilities. In our simulations we are able to attain a full bunch length of 20-30 degrees, while the output energy can vary from 2 to 4 MeV. Simulations as well as a preliminary design will be presented.