Agile methods are extensively adapted by software development organizations due to the competitive benefits it offers. In recent years global software development (GSD) projects practice agile methods as prominent methods to deliver the software in increments with utmost user satisfaction and affordable cost. Beside the use of agile methods, the software industry has also considered the green aspect of software, to be in line with the demands of the organizations and the world technological ecosystem. The green and sustainable feature of software should focus both the energy and resource efficiency key factors. This phenomenon of embedding the green flavor in software has emerged a new research area, green software engineering, that promises the development of eco-friendly software with minimum energy and use of less computing resources, to trim down the adverse effects on both society and environment. The principal objective of this research study is to design and develop a multi-level Green-Agile Maturity Model (GAMM) to assess the GSD vendors' agile maturity in terms of green software development. The model has been built in four phases. In phase I and II, systematic literature review (SLR) was performed to identify the success factors and risk factors that either supports or hinders the green and sustainable software development respectively by practicing the agile methods in GSD. The results have been validated from 106 relevant experts, dealing with agile and green software projects, through questionnaire survey. The experts' demographic represents 25 different countries. We also identified the industry practices through SLR and survey, to address our identified critical factors. Phase III of this research deals with development of the GAMM by categorizing the identified factors into seven Green-Agile maturity levels. A similar approach has been used in other models such as Capability Maturity Model Integration (CMMI), Implementation Maturity Model (IMM) and Software Outsourcing Vendors Readiness Model (SOVRM). In phase IV of this research, five case studies were conducted at GSD organizations, to evaluate the structure and efficacy of the GAMM, while as a major contribution, this paper presents our developed model, the GAMM, which aims to assess the green-agile maturity of the GSD vendors in terms of green and sustainable software development. INDEX TERMS Agile software development, Green and sustainable software, Green-Agile Maturity Model (GAMM), Global software development (GSD), Agile methods