The joint clearance can be the mainly concern factor in the analysis of repeatability of positioning for a manipulator. Traditionally, the joint clearance is empirically assumed to be uniform or normal variables. This hasty treatment may be not accurate enough when the precise statistic information of variables cannot be obtained. To handle the reliability evaluation problem with arbitrarily distributed joint clearances, a moment-matching based method is proposed. The highly nonlinear performance function is firstly established by the forward kinematics and then a second order Taylor expansion is performed on this function for the order reduction. Based on the maximum entropy principle, the Lagrange multipliers method is employed to derive a best-fit probability density function (PDF) with consideration of the first four moments-matching restrictions. This study shows that the prosed method can acquire a better accuracy and efficiency compared with the first order second moment method (FOSM), first order reliability method (FORM) and Monte Carlo simulation (MCS). A serial manipulator is applied as an example to demonstrate the new method.