Space charge in a point cathode thermionic emission gun has been studied with numerical method. The method is an iterative one, consisting of the field determination using the integral form of Poisson's equation, the direct ray tracing in 3D, and the estimation of space charge from the traced rays. The rays are traced for limited emitting conditions. The estimated space charge is treated as a number of the coaxial charged rings with different radii and positions. Using the method, the potential distribution around the cathode tip was examined at different cathode temperatures. The numerical results at the cathode temperatures of 2800 K and 2950 K are given, and the influence of space charge is discussed.