LAM (Laser Assisted Machining) has several advantages, such as high productivity, reduction of manufacturing cost, high quality, and a narrow HAZ (Heat Affected Zone). Studies on LAT (Laser Assisted Turning) have been largely conducted in recent years. However, there have been certain limitations in performing studies that focus only on the LAT of cylinder shapes throughout the world. Therefore, LATM (Laser Assisted Turn-Mill) is proposed in this study for machining complex geometries, such as square and spline members. In the case of LATM processes, it is more difficult to estimate the temperature after completing a preheating process because it represents an elliptical shape as a laser heat source is inclined. A new laser heat source projection method is proposed for the analysis of such square and spline members. The temperature distribution of the members based on their rotation is predicted. The results of the analysis are compared with that of LATM experiments. The results reveal that the cutting force in machining SM45C is reduced by about 8-14%, while the surface roughness is reduced by about 25-40% compared with that of conventional turn-mill processes.