On-body wireless networks (oBWNs) play a crucial role in improving the ubiquitous healthcare services. Using oBWNs, the vital physiological information of the patient can be gathered from the wearable sensor nodes and accessed by the authorized user like the health professional or the doctor. Since the open nature of wireless communication and the sensitivity of physiological information, secure communication has always been the vital issue in oBWNs-based systems. In recent years, several authentication schemes have been proposed for remote patient monitoring. However, most of these schemes are so susceptible to security threats and not suitable for practical use. Specifically, all these schemes using lightweight cryptographic primitives fail to provide forward secrecy and suffer from the desynchronization attack. To overcome the historical security problems, in this paper, we present a lightweight and secure three-factor authentication scheme for remote patient monitoring using oBWNs. The proposed scheme adopts one-time hash chain technique to ensure forward secrecy, and the pseudonym identity method is employed to provide user anonymity and resist against desynchronization attack. The formal and informal security analyses demonstrate that the proposed scheme not only overcomes the security weaknesses in previous schemes but also provides more excellent security and functional features. The comparisons with six state-of-the-art schemes indicate that the proposed scheme is practical with acceptable computational and communication efficiency.