This paper aims to propose a new guidance algorithm for intercepting a high-speed target with time-varying acceleration, such as a tactical ballistic missile that flies in a quasi-ballistic trajectory. The motivation of this study lies in the fact that the classical proportional navigation guidance (PNG) undergoes performance degradation under the above engagement scenario due to its intrinsic property. To deal with the issue, through the closed-form trajectory solutions of the bias PNG (BPNG) command, we first deduced the relationship between the predicted LOS rate in the BPNG command and the predicted look angle corresponding to the collision triangle and then find a significant physical constraint to achieve zero miss-distance and zero terminal acceleration. Based on this concept, an accurate collision course that reflects the motion characteristics of the ballistic target and missile is first analyzed. The predicted look angle that leads to achieving the accurate collision course is then determined with the help of a novel time-to-go calculation method. Finally, the proposed guidance law providing the predicted look angle is obtained by leveraging the concept of biased PNG. Since the proposed method is designed to achieve an accurate collision course, it does not lead to unnecessary maneuvering near the target under the engagement scenario. This property is desirable for reserving the operational margin of maneuverability for reacting to unexpected situations during the engagement. It could improve the capturability of the target. Finally, the performance of the proposed method is verified through numerical simulations in a way to compare with the existing methods such as PNG and the augmented PNG (APNG). Moreover, the concept of the proposed guidance algorithm is applied to the terminal homing guidance algorithm for intercepting the ballistic missile in boosting/ascending phase. It is also confirmed by numerical simulations that the proposed algorithm has better performance than PNG and APNG. In addition, the robustness is confirmed by analyzing the effect of estimation errors of the main target information and the proposed algorithm is exapnded to 3D space to increase the practicality.