Dimensional and profile measurements of deep-hole parts are key processes both in manufacturing and product lifecycle management. Due to the particularity of the space conditions of deep-hole parts, the existing measurement instruments and methods exhibit some limitations. Based on the multi-axis, highly precise servo drive system, a novel measuring device is developed. The laser displacement sensors are fed by the flux-switching permanent magnet linear motor, and the part is rotated by the servo motor. On this basis, the assessment methods of roundness, straightness, and cylindricity are proposed by employing the least square method (LSM). Additionally, considering the axial center deviation between the sensors and the part, the rotating center coordinate is optimized by the gradient descent algorithm (GDM). Then, the measurement system is constructed and the experiment study is conducted. The results indicate favorable evaluation error of the LSM fitting and GDM iteration. Compared with the coordinate measuring machine (CMM), the measured results show good consistency. In the error analysis, the angle positioning error of measured point is less than 0.01°, and the axial positioning error is less than 0.05 mm. The proposed system and assessment method are regarded as a feasible and promising solution for deep-hole part measurements.