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.