The advances of the Internet of Things (IoT) have had a fundamental impact and influence in sharping our rich living experiences. However, since IoT devices are usually resource-constrained, lightweight block ciphers have played a major role in serving as a building block for secure IoT protocols. In CHES 2015, SIMECK, a family of block ciphers, was designed for resource-constrained IoT devices. Since its publication, there have been many analyses on its security. In this paper, under the one bit-flip model, we propose a new efficient fault analysis attack on SIMECK ciphers. Compared to those previously reported attacks, our attack can recover the full master key by injecting faults into only a single round of all SIMECK family members. This property is crucial, as it is infeasible for an attacker to inject faults into different rounds of a SIMECK implementation on IoT devices in the real world. Specifically, our attack is characterized by exercising a deep analysis of differential trail between the correct and faulty immediate ciphertexts. Extensive simulation evaluations are conducted, and the results demonstrate the effectiveness and correctness of our proposed attack.