For high-precision machining, a convenient and accurate detection of motion error for machine tools is significant. Among common detection methods such as the ball-bar method, the laser tracker approach has received much more attention. As a high-accuracy measurement device, laser tracker is capable of long-distance and dynamic measurement, which increases much flexibility during the measurement process. However, existing methods are not so satisfactory in measurement cost, operability or applicability. Currently, a plausible method is called the single-station and time-sharing method, but it needs a large working area all around the machine tool, thus leaving itself not suitable for the machine tools surrounded by a protective cover. In this paper, a novel and convenient positioning error measurement approach by utilizing a single laser tracker is proposed, followed by two corresponding mathematical models including a laser-tracker base-point-coordinate model and a target-mirror-coordinates model. Also, an auxiliary apparatus for target mirrors to be placed on is designed, for which sensitivity analysis and Monte-Carlo simulation are conducted to optimize the dimension. Based on the method proposed, a real experiment using single API TRACKER 3 assisted by the auxiliary apparatus is carried out and a verification experiment using a traditional RENISHAW XL-80 interferometer is conducted under the same condition for comparison. Both results demonstrate a great increase in the Y-axis positioning error of machine tool. Theoretical and experimental studies together verify the feasibility of this method which has a more convenient operation and wider application in various kinds of machine tools.