This paper considers on-demand WiFi wake-up where a wake-up receiver is installed into each WiFi device. The wake-up receiver detects a wake-up call by finding the predefined length of WiFi frames, which corresponds to a wake-up ID, through envelope detection with limited signal processing. Since each wake-up receiver continuously observes the WiFi channel, an adverse event of False Positive (FP), where a WiFi device is falsely turned on without actual wake-up calls, can occur when the length of non-wake-up, background data frames match with predefined length. In this paper, we suggest using the received signal strength (RSS) of WiFi frames to differentiate the real and false wake-up calls. The proposed scheme exploits the correlation among RSSs of WiFi frames received from a single station located in a fixed position. Using measured RSS data obtained under various settings and different degrees of mobility, we investigate not only the FP reduction rate but also its impact on the probability of detecting real wake-up calls. We also present experimental results obtained with our prototype in which the proposed scheme is implemented.