In the mobile distributed environment, an entity may move across domains with great frequency. How to utilize the trust information in the previous domains and quickly establish trust relationships with others in the current domain remains a challenging issue. The classic trust models do not support cross-domain and the existing cross-domain trust models are not in a fully distributed way. This paper improves the outstanding Certified Reputation (CR) model and proposes a Lightweight Cross-domain Trust (LCT) model for the mobile distributed environment in a fully distributed way. The trust certifications, in which the trust ratings contain various trust aspects with different interest preference weights, are collected and provided by the trustees. Furthermore, three factors are comprehensively considered to ease the issue of collusion attacks and make the trust certifications more accurate. Finally, a cross-domain scenario is deployed and implemented, and the comprehensive experiments and analysis are conducted. The results demonstrate that our LCT model obviously outperforms the Bayesian Network (BN) model and the CR model in our cross-domain scenario, and significantly improves the successful interaction rates of the honest entities without increasing the risks of interacting with the malicious entities.