Parallel three dimensional (3D) coordinate measuring machine (CMM) has characteristics of a large measurement range and high accuracy. A tetrahedron CMM was described which can measure the position of a point in space or machine tool by aimed at these characteristics. There were some measurement errors existed in the CMM due to the geometric errors and the error of inevitable gaps of Telescopic rod at all levels. A measurement error model of the CMM was established by aimed at the error of Telescopic rod length, and through MATLAB software, the measurement errors of CMM space were analyzed with simulation so as to obtain error telescopic law of workspace of machine tool in the CMM. By analysis with calculation, it is obtained that the error of Telescopic rod length and measured initial position errors which impacted on the measuring machine error are only between 02%~15%, and meet the measurement requirements.