In recent years, software trustworthiness has been a focus of interest for researchers. A more consensus view is that software trustworthiness is the degree of how software behavior is accordant with people's expectation. The quality is formed in the process. Obviously, the evidences that build the confidence of software quality are presented in software process too. The process subjects, behaviors and the various methods to guarantee the quality of process products provide the basic evidences to establish the software trustworthiness. Evidence-based decision-making and management is the core of the modern theories of quality. Thus, both evidence-based and data-driving software engineering approaches have tried to address the problem from the perspective of objective data. Under the support of national natural science foundation of China, this study presents a software process trustworthiness model for building the confidence from the view of software processes. As the important and fundamental part in the model, evidence is used to transfer the trust chain bottom-up and to support the evaluation of trustworthiness of software process. Focusing on evidence system in the model, this study complies with four principles including integrity, necessity, compatibility and sustainability. According to the basic requirements of process management, it investigates CMMI and other software process reference models to refine and cross-examination the evidences, create some new evidence to adapt open source software development and extend some evidence to enhance the trustworthiness of process. The study develops an evidence system with high credibility, objectiveness and comparability. The presented evidence system can establish the trustworthiness from three dimensions:process subjects, process behaviors and process products. It also covers the whole lifecycle of software development. Combined with other parts of the trustworthiness model, it can support the evidence-based, bottom-up trustworthiness evaluation of software process. The presented model can be widely applied in software industry.