Parts with rapidly varied geometric features are usually crucial parts in high-end equipment and widely applied in the fields of aerospace, energy and power, which are difficult or inefficient to process because of the more special structure and the higher requirement of machining precision. High-speed machining technology provides an effective method for parts with rapidly varied geometric features to solve the contradiction between high demand and low machining efficiency. However, as the existence of rapidly varied geometric features, the machining toolpath for such parts is always complex free-form curve and the actual moving speed of the workbench of the NC machine tool cannot reach the feed-speed set in the NC program timely due to the drive constraint of NC machine tool. Furthermore, the machine tool would vibrate violently when machining the rapidly varied geometric features. In this way, the big machining error will be formed. A machining error reduction method by combining of feed-speed optimization and toolpath modification in high-speed machining for such parts is proposed. First, considering that the actual feed-speed cannot reach the programmed value when the toolpath curvature is too large, the feed-speed is optimized with the constraints of jerk and acceleration limitations of the feed shafts, and a feed-rate smoothing algorithm is applied. Then, the compensated cutter locations are calculated via machining-error estimation. Finally, the modified NC codes are acquired according to the optimized feed-speed and the compensated toolpath. By combining the feed-speed optimization and toolpath modification, the high precision and high efficiency machining can be realized. The experimental results demonstrate the feasibility of the proposed approach. This study provides an effective approach to reduce the machining error in high-speed machining, and is significant for improving the processing precision and efficiency of parts with rapidly varied geometric features.