Internet of Things (IoT) has gradually become one of the most important platforms across different disciplines, by enabling dedicated physical objects to communicate with other Internet-enabled things. With this trend, more devices in medical environments are capable of connecting with each other, named Internet of Medical Things (IoMT). It aims for improving efficiency and reducing communication delay, e.g., monitoring the status of patients and notifying abnormal events. However, due to the distributed nature, insider attacks are still one of the major threats to such IoT environment. How to improve the trust management in IoMT remains a challenge. Motivated by the popularity of blockchain technology, in this paper, our general goal is to investigate the performance of blockchain-based trust management. In particular, we focus on a particular type of IoMT, named medical smartphone networks (MSNs), because of the wide adoption of smartphones in the medical domain. Then, we apply blockchains for enhancing the effectiveness of Bayesian inference-based trust management to detect malicious nodes in MSNs. In the evaluation, we explore the performance of our approach in two different healthcare environments, and experimental results demonstrate that blockchain technology can help improve the detection efficiency of detecting malicious nodes with reasonable workload.