This paper aims to propose a new guidance algorithm for intercepting a high-speed maneuvering target, 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 the performance degradation under the above engagement scenario due to its intrinsic property. To deal with the issue, an accurate collision course that reflects the motion characteristics of the ballistic target and missile is first analyzed. The desired 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 desired look angle is obtained by leveraging the concept of the 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).