Multi-axis Laser Engraving Machine Tools (LEMT) are widely used in precision processing of parts with complex surface. The accuracy of kinematic model and parameter measurement are the key factors determining the processing quality of LEMT. In this paper, a kinematic model of multi-axis LEMT was established based on Homogeneous Transformation Matrix (HTM). Two types of unknown parameters, linkage parameters and positioning parameters, were measured in the presented model. Taking advantage of the characteristics of laser processing, this paper proposed a rapid measurement method of linkage parameters by combining the machine tool motion with the laser marking action. For positioning parameters, this study proposed a non-contact measurement method based on structured light scanner, which can obtain the translation values and the rotation values from the Workpiece Coordinate System (WCS) to the Basic Coordinate System (BCS) simultaneously. After the measurement of two kinds of parameters of a multi-axis LEMT was completed, the processing of a spatial curve was performed and the average contour error was controlled at 15.1 µm, which is sufficient to meet the project requirements.