In order to study the positioning accuracy of the header of three dimensional (3D) printer with respect to the hot bed in the influence of all errors, a Monte Carlo method was used to evaluate the positioning accuracy. The topological construction model of 3D printer was built according to the multibody system theory. Based on the instrument precision theory, an integrated error propagation model of the 3D printer was built to analyze the comprehensive effect of the various error sources, the error vector in x, y and z directions during the step motor moving was analyzed. The positioning accuracy of the header with respect to the hot bed was calculated with simulation by Monte Carlo method. The results show that within the believed 95% probability, the position outputs and the expanded uncertainty in x, y and z directions of the printer head with respect to the hot bed were calculated: x=(70±0099) mm, y=(50±0100) mm, z=(20±0518) mm. This method can be used to analyze the main error source which influenced the positioning accuracy, and compensated it so that improving the positioning accuracy of 3D printer. This method can also be used in the precision machine design, to specify subsystem precision requirements to achieve an overall balance in the levels of accuracy index of multibody rigid structure.