In this investigation, a novel three-degree-of-freedom laser interferometer is proposed which enables to determine the motion parameters including linear displacement, horizontal and vertical straightness in a linear axis. The modified common-path Fabry-Pérot interferometer consists of two optical arrangements for measuring the linear displacement and the straightness respectively. In the optical arrangement of the linear displacement measurement, the one eighth waveplate in the Fabry-Pérot optical cavity constructed with a planar mirror and a corner cube retro-reflector (CCR) is employed to form the orthogonal phase shift between interferometric signals and then they can be acquired by two photodiodes (PDs) to detect the linear displacement. In the other optical arrangement, a quadrant photodetector (QD) serves to inspect the lateral displacements induced by the dynamic offset of CCR. Furthermore, the relevant measuring characteristics of the self-developed laser interferometer are compact optical arrangement, convenient operation and efficient inspection. It would be beneficial for the linear positioning measurement and calibration of precision machines, e.g., linear positioning stages or high precision machine tools.