Adaptive cruise control (ACC) systems, which detect distance of a preceding vehicle and a radar-mounted vehicle using the radar, are available from automobile manufacturers. The distance and a relative velocity of the preceding vehicle and the radar-mounted vehicle can be estimated by analyzing a millimeter-wave signal obtained through the radar. Due to a characteristic of the radar and the relative velocity between the preceding vehicle and the radar-mounted vehicle, it is difficult to detect and track the preceding vehicle in the same lane where the radar-mounted vehicle is moving. In this paper, an algorithm is proposed to solve the above difficulties. The proposed algorithm separates a radar-search range into several blocks. And it detects and tracks a preceding object as a detected block of the several blocks. Applying this algorithm and assigning priority among the blocks, the searching range for the targeting vehicle and response time of the system are reduced.