If it is necessary to punish the legitimate transmitter Alice in time, warden Willie must make a corresponding decision before the end of the transmission. Therefore, in the binary hypothesis test framework, we consider the timeliness of Willie’s detection in covert communications for the first time. Specifically, we consider Willie adopting a truncated one-sided sequential probability ratio test (TOSPRT). By analogy with the KL divergence in the FSS detection framework, we demonstrate that the Chernoff information is a correct and reasonable metric as the covert constraint. The key indicators of the three-node model of finite blocklength covert communications are analyzed. Further, to maximize the communication rate between Alice and the receiver Bob, we optimize the transmission power and blocklength of Alice subject to the covert constraint. Theoretical analysis and simulation results show that the maximum covert information can be transmitted when the blocklength reaches the maximum.