The emission characteristics of a point cathode thermionic electron gun have been studied with numerical method. The method is based on the integral form of Poisson equation. The field including the space charge is obtained by the iterative procedure, consisting of the field calculation, the electron ray tracing in 3D, and the determination of the space charge from the rays. The space charge distribution was determined from the rays traced with random emitting conditions considering energy and angular distributions and treated as many coaxial ring charges. The use of random emitting conditions leads to a self-consistent result after several iterations. The emission currents were calculated for different bias voltages and different cathode temperatures. The method provides the emission currents close to the measured values. [DOI: 10.1380/ejssnt.2006.339]