Recently, much attention has been paid to optical components with complex surfaces because they can significantly optimize the aberrations of optical systems. However, a complex surface introduces several difficulties for precise measurement. To address this challenge, we propose tilted-wave point diffraction interferometer (TPDI) for measurements of complex surfaces. TPDI combines the advantages of tilted-wave interferometry and point diffraction interferometry, thus enabling high-precision measurements of complex surfaces; moreover, this method has demonstrated good efficiency and versatility. We adopt a fiber array (FA) to generate diffractive tilted waves to compensate for the local gradient of the test specimen. Unlike the classical PDI, which focuses more on the beam quality of the on-axis diffractive wave, the proposed system requires better quality for both the on-axis and off-axis diffractive waves. Therefore, the main parameters of the FA that may introduce measurement errors are analyzed, including the end face roughness of the array, the quality of diffractive wavefronts, and the initial optical path differences. Finally, the measurement result of the high-order hyperboloid verifies that our TPDI is effective and its precision of testing a complex surface is better than λ  /  37 (rms, λ  =  632.8  nm).