Parts with the complex curved surface are commonly-used in high-end equipment. The machining quality of the complex curved surface parts is important for the property of high-end equipment. With position control of the main spindle i.e. C axis, the slow tool servo (STS) turning is a very promising technique to effectively machine complex curved surface parts. However, the turning machining quality is restricted by the cutting force fluctuation in finishing turning. Hence, the STS turning toolpath generation approach with the constraint of the cutting force fluctuation is proposed in this study. As the cutting force is proportionate to the cutting area, the cutting area for turning complex curved surfaces is analyzed and calculated. Then the functional relation between the cutting force fluctuation and the feed rate is derived. Based on the geometrical characteristic of the first revolution of toolpath, the feed rate is optimized with small cutting force fluctuation to derive the cutter contact points (CCPs) of toolpath in the cylindrical coordinate system. Then the cutter location points (CLPs) of STS turning toolpath are calculated with tool nose radius compensation. From the validation experiment results, it can be seen that the cutting force fluctuation, the profile tolerance and the surface roughness of parts are effectively reduced, and the surface roughness of the part machined with the proposed toolpath planning method is 17.625 nm. Thus, this study provides guidance for toolpath generation with constraint of the fluctuation of the cutting force in STS turning for a complex curved surface.