Three branched chain of the 3-RCR parallel robot were analyzed based on the screw theory of motion screw and constraint screw. The degree of freedom (DOF) of the mechanism was calculated. The solution of direct position and the inverse position of the 3-RCR parallel robot were obtained by the established position equation from the transformation of the static coordinate system and the moving coordinate system. By using the solution of MATLAB software programming, the numerical example of the solution of direct position and the inverse position is given.