The trustworthiness of software is determined by both its functional requirements and non-functional requirements. Especially, the non-functional requirements are the determinants of the trustworthy software that show how it achieves the users' desired goals. Considering the importance of trustworthy software and the urgent needs for it, an approach to obtaining process strategies for trustworthy software in the early phase of requirements engineering is proposed. Firstly, the definition of trustworthy software requirements is defined as the combination of the trustworthiness requirements and the quality requirements. Trustworthiness requirements are defined as both functional requirements and trustworthiness concerns. Quality requirements are defined as soft goals. Then, based on fuzzy set theory and information entropy, acquisition method of trustworthiness concerns and soft goals is proposed. On this basis, process strategies for obtaining framework are proposed. Unlike the traditional early-phase requirements engineering which focuses on technical and design decisions, the aim of this study is to make process decisions to support trustworthy software development. In addition, to address the conflict relationships of the non-functional requirements, a reasoning method is developed for solving satisfiability problems of non-functional requirements in trustworthy software. Finally, through analyzing a trustworthy third-party certificate authority software case, feasibility of the proposed approach is described.