Internet of Things (IoT) is widely used as a fundamental technology for realizing various services. An IoT-based service system comprising cloud servers and many IoT devices connected via networks may be risky owing to the possibility of the entire system being be affected by cyberattacks on an IoT device. Moreover, new software vulnerabilities are frequently reported. From the perspective of security, IoT device software must be reliable and resilient. Consequently, a secure software update mechanism for IoT, assurance of software reliability, and mitigation mechanisms are required. Overall, this study proposed a zero-trust over-the-air (ZT-OTA) update framework for the reliable and resilient software update management of IoT devices via OTA software updates from remote locations. The ZT-OTA update framework provides a strict software version-management mechanism that enhances the security of software updates. Further, the proposed framework collaborates with a Software Assessment Service (SAS) as an authorized third-party assessment organization and deploys reliable software approved by the service to IoT devices. Upon discovering a software vulnerability following the deployment of the software, the SAS proactively revokes the reliability of the software by revoking its certificates for signing software codes and the vulnerability assessment result. Subsequently, the ZT-OTA server notifies developers and users of IoT devices to arrange for new software that must be fixed and automatically acts on behalf of IoT devices that must be retired. This study introduces the detailed design of the ZT-OTA update framework and describes to demonstrate its feasibility.