The integration of social networking concepts into the Internet of Things (IoT) has led to the so called Social Internet of Things paradigm, according to which the objects are capable of establishing social relationships in an autonomous way with respect to their owners. Within this scenario, “things” interact opportunistically with their peers to seek needed services. However, attacks and malfunctions in the IoT can outweigh any of its benefits if not handled adequately. In this article, we focus on the possible types of trust attacks that can affect the IoT and propose a trust management model able to overcome all the analyzed attacks. Simulations show how the proposed model can effectively isolate almost any malicious nodes in the network at the expense of an increase in the number of transactions needed for the model to converge.