Most tool paths in Computer Numerical Control (CNC) machining consist of a large amount of linear motion commands (G01). However, the discontinuity of curvatures and feedrates at corner junctions will cause machine tool vibration, resulting in a decreased surface quality and processing efficiency. Therefore, smooth corner transitions within specified tolerances and machine tool motion constraints are required during the interpolation process. In recent years, corner transition methods have evolved from simple corner removal to performance improvement, leading to the development of kinematics-based direct velocity planning methods that fully utilize the motion capabilities of each axis. However, most kinematics-based methods decelerate first and then accelerate at corners, limiting the potential velocity improvements. We propose a novel jerk-confined interpolation algorithm that can achieve persistent acceleration at a series of corners. First, a two-phase asymmetric corner smoothing model for accelerating/decelerating(acc/dec) transitions at corners is introduced. Next, an optimal 7-stage S-shaped acc/dec algorithm is proposed for the remaining straight-line segments, which can be applied when the acceleration at both ends is not zero. Additionally, by a bidirectional planning adjustment strategy, we can look forward and backward several adjacent corners, and then determine the optimal acceleration state that can be achieved at each corner, even when the two corner points are close to each other. Our method significantly improved the machining efficiency of machine tools. For a “clover” curve (See Fig. 1), our method can reduce the machining time by 52.4% compared to the method with constant jerk at corners[1](AU), 18.8% compared to the method with zero acceleration at the corner conjunction[2](KCS), and 6.7% compared to the asymmetric corner smoothing method[3](ASYM). Furthermore, using a look-ahead smoothing algorithm for computation results in short calculation times and low costs, we can obtain the real-time requirement in CNC machining. The experimental results have proven the effectiveness and efficiency of the method.