It is known that software system plays an important role in the information society, and high trustworthiness is a key requirement for many types of systems, such as safety critical systems, telecommunication systems, and mission critical software systems. How to improve the trustworthiness to better serve our society has become an important research focus among areas of software theory and technology application. Considering these, the paper establishes a trusted evaluation model making use of the fuzzy grey comprehensive evaluation method to evaluate the software trustworthiness. A banking system is evaluated by the trusted evaluation model and the evaluation results prove the feasibility and effectiveness of the model in dealing with the fuzzy and gray nature of experts' judging information.