The cam-gear-linkage combination mechanism was used in the new model thread-taking-up mechanism of computerized embroidery machines. The calculation model of the thread-taking-up location accuracy analysis was established by using mechanism analysis method. The thread-taking-up accuracy of the thread-taking-up mechanism was analyzed in detail. The numerical differentiation formula for thread-taking-up accuracy was obtained, the MATLAB computer program is developed, and a practical calculation has been made of the new thread-taking-up mechanism. The rule of thread-taking-up accuracy along with the change of the crank angle was presented, which has provided a very important reference for mechanism kinematics design in thread-taking-up mechanism of computerized embroidery machines as well as for enhancing the embroidery quality.