For the geometric error elements of three-axis CNC machining center which greatly affect the machining precision, the spatial geometric error fields were analyzed, and the universe simulation software of error fields was developed. Firstly, error elements were analyzed based on multi-body theory;the spatial geometric error fields of machining center were modeled according to the topological structure of the machining center. It can be seen that the models of spatial geometric error fields were closely relative to the types and the positions of axes in the working piece chain and tool chain of the machining center. The models were different for machine centers with different topological structures. Then, the simulation software of error fields for universe three-axis CNC machining centers was developed due to the modeling process using Visual Studio platform in order to conveniently analyze the different machining centers. The software can realize the visualization of error fields and generate the compensated machining code based on the nominal code. It can give help for the structural design and error compensation of machining centers. Finally, the simulation software was applied to Carver800T vertical machining center. The error fields of this center were analyzed with all measured geometric error data to obtain the error distribution curve and the whole error fields of the machine tool. The compensated machining code was also obtained based on the nominal code of workpiece and the error fields of this machine center. It provided basis for the precision improvement and error compensation of machining center.