In recent years, web service composition attracts huge academic attention and is regarded as a promising area to help automatically actualize complex on-line business processes. While many composition models and frameworks are proposed, little research is conducted on the trust issues of the web service composers (WSCs). In this paper, we first discuss the necessity of the research on the trust issues of web service composers. Then we propose a trust computation framework that integrates both service-level and composer-level trust factors to calculate the trustworthiness of web service composers. Service-level and composer-level trust factors are discussed. The computational logics for each trust factor and for their integration are presented. We also use experimental environment to evaluate the effectiveness of our proposed framework.