Direct mesh machining has been an effective technique in rapid manufacturing. Currently, the cutter location path generation is an effective method for the direct mesh machining. However, this method may cause surface defects, such as the overcut-slot, the transit-pit, and the facet defects. Therefore, the application of this method is limited for the machining accuracy issue. From the comprehensive analysis of cutter location path generation and the inspection of the machined parts by the mesh offset intersection (MOI) algorithm, the tessellation error of the offset mesh is the main factor causing the machining surface defects. To solve the problem, we propose an improved MOI algorithm to reduce the influence of tessellation error. Compared with the original surface, only the mesh vertices are considered as the points without tessellation error. Therefore, we revise the algorithm through calculating the cutter location points only from the vertices and smoothing the tool-path in two perpendicular directions. This improved algorithm includes two sub-algorithms: a vertex-based cutter location point calculation sub-algorithm and a bi-directional spline interpolation sub-algorithm. To validate the effectiveness of the improved algorithm, the machining accuracy is investigated and verified through several testing parts. The experimental results show that the improved MOI algorithm can effectively improve the machining accuracy and avoid surface defects on the work-piece surfaces.