By leveraging the advancements in Information and Communication Technologies (ICT), Smart Grid (SG) aims to modernize the traditional electric power grid towards efficient distribution and reliable management of energy in the electrical domain. The SG Advanced Metering Infrastructure (AMI) contains numerous smart meters, which are deployed throughout the distribution grid. However, these smart meters are susceptible to cyberthreats that aim to disrupt the normal operation of the SG. Cyberattacks can have various consequences in the smart grid, such as incorrect customer billing or equipment destruction. Therefore, these devices should operate on a trusted basis in order to ensure the availability, confidentiality, and integrity of the metering data. In this paper, we propose a Markov chain trust model that determines the Trust Value (TV) for each AMI device based on its behavior. Finally, numerical computations were carried out in order to investigate the reaction of the proposed model to the behavior changes of a device.