In this paper we propose a trust algorithm, dubbed NeuroTrust, based on a multi-layered neural network. Previous work introduced trust as a performance estimation algorithm between team members in multi-agent systems, to allow for behavior optimization of the team. The trust model was developed based on an Acceptance Observation History (AOH) and confirmation and tolerance parameters to control trust growth and decay. Further work proposed certain improvements, in an autonomous vehicles convoy scenario, by considering agent diversity and a non-linear relationship between trust and vehicle control. In this work we show a further optimization using a deep recurrent neural network. This multi-layered neural network delivers trust as a probability function estimation with AOH as a sliding window batch input. The neural network is pre-trained using supervised learning, to emulate the previous trust model, as baseline. This pre-trained model is then exposed to future optimization using on-line reinforcement learning. The proposed trust model could be adaptable to a variety of systems, external conditions, and agent diversity. One application example where such a biologically-inspired trust model is suitable would be for soldier-machine teaming. Furthermore, particularly in the autonomous convoy scenario, we can account for the trust-control relationship nonlinearity in the trust domain, thus simplifying the control algorithm.