This paper investigates the kinematic calibration of a 3-DOF parallel mechanism based on the minimal linear combinations of error parameters. The error mapping function between the geometric errors and the output errors is formulated and the identification matrix is generated and simplified. In order to identify the combinations of error parameters, four theorems to analyze the columns of the simplified identification matrix are introduced. Then, an anti-disturbance index is presented to evaluate the identification performance. On the basis of this index, measurement strategy is developed and optimal measuring configurations are given. After external calibration, linear interpolation compensation is applied to improve the terminal accuracy further. Results of experiment show that the method used in this paper is effective and efficient, and the errors are convergent within two iterations generally. This method can be extended to other parallel mechanisms with weakly nonlinear kinematics.