Curving tool paths composed of straight lines, which are often represented as G01 blocks, are still the most widespread format form in the machining process chain of CAD/CAM/CNC. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. In this paper, a real-time look-ahead interpolation methodology is proposed, which adopts a curvature-continuous PH curve as a transition to blend corner at the junction of adjacent lines in the tool path. The blending algorithm can guarantee the approximation error exactly, and the control points of the curve can be calculated analytically. On the other hand, the arc length and the curvature of the transition curve, which are important items in speed planning, also have analytical expressions. All the advantages are the guarantee of calculation efficiency during the interpolation. Except for a curvature-continuous tool path, our look-ahead algorithm adopts a speed planning window strategy to achieve a balance between the calculation capabilities and the real-time interpolation requirements. In this window, the corner transition algorithm and speed planning are implemented simultaneously and dynamically during the interpolation. By defining the width of this window, which is actually the number of linear segments contained in this window, can adjust the time consuming of speed planning. Simulation and experiments on our own developed CNC platform are conducted. The results demonstrate the feasibility and efficiency of the proposed algorithms.