The finite number of angles used in a discrete ordinates solutions to a transport problem may lead to an anomaly known as the "ray effect". A successful method which has been used widely to mitigate ray effects is to analytically compute the first collision source in a medium and use it as a distributed source in the discrete ordinates code. In the present paper the two-dimensional GRTUNCL code which has been widely used for the geometry having the symmetry around Z-axis has been converted to compute the uncollided fluence at each spatial mesh in an R-8-Z grid and to generate the associated distributed first-collision source moments for use as a distributed source in the TORT three-dimensional discrete ordinates computer code. This coupled GRTUNCL-3D and TORT code system has been shown that it can mitigate the ray effect for a three dimensional geometry which has no symmetry around Z-axis.