This study investigated the effect of a secondary task when a takeover request (TOR) is received from an automated driving car, with a focus on nature of the secondary task (active or passive). Participants were asked to engage in one type of secondary task during automated driving, and we measured 1) forward gaze and 2) latency after the TOR to switch from automated to manual operation. Playing a game with a smartphone (active task) decreased driving-related performance in terms of shorter forward-gaze duration and longer delays in switching from TOR. In contrast, the performance in the other tasks (passively watching a video and conversing with another person) was little different from that in a condition with no secondary task. Compared to the tasks, not an active but a passive task would contribute to maintain the readiness for TOR.