The laser triangulation probe conveniently obtains surface topography data of a measured target. However, compared to the touch probe, its reliability and accuracy can be negatively affected by various factors associated with the object being measured and the probe itself. In this paper, to identify potential compensation strategies to improve the accuracy of depth measurement for laser triangulation probe, the measuring errors caused by an oil film on the measured surface, and the probe’s position and orientation parameters with respect to the measuring object (including scan depth, incident angle, and azimuth angle), were studied. A theoretical model based on the geometrical optics, and an empirical model from the error evaluations, were established to quantitatively characterize the error influence of oil film and probe’s parameters, respectively. We also investigated the influence pattern of different filtering methods with several comparison experiments. The verification procedures, measuring both a free-form surface (chevron-corrugated plate) and a gauge block covered with an oil film, demonstrate that these models and measurement suggestions are viable methods for predicting theoretical error and can be used as compensation references to improve the accuracy of depth measurement to the laser triangulation probe.