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B-spline curve approximation is widely used for fitting linear toolpaths to improve machining quality and efficiency in CNC machining. For a high-quality smoothing method, the control of both approximation error and curve curvature needs to be taken into account. To reduce the maximum curve curvature while meeting the precision requirements, a B-spline approximation scheme with tool tip position adjustment is proposed in this paper. Toolpaths are first divided into several subdivisions according to the discrete curvature of each tool tip point. For subdivisions that need adjustment, tool tip positions are adjusted to minimize the maximum discrete curvature. An existing approximation method named energy-term-incorporated progressive and iterative approximation for least square fitting (ELSPIA) is selected and improved to fit the adjusted toolpaths and lower the chord errors. For improving the numerical stability of the ELSPIA method, the way of searching appropriate foot point parameters is discussed in this paper. Deviation expansion factors of tooltip points are also defined to make the ELSPIA method suitable for fitting the adjusted toolpaths. Both simulations and experimental studies are conducted to prove that the proposed method can significantly decrease the maximum curvature of fitted B-spline curves and improve the machining efficiency without exceeding the tolerance. For example, experimental results show that for the tested butterfly and rabbit toolpaths, the proposed method can improve the machining efficiency by 2.61% and 2.37%, compared with the ELSPIA method without tool tip position adjustment. [ABSTRACT FROM AUTHOR]