Sustainability is one of the most important quality factors and it integrates some other quality factors in the product too. Moreover, it makes an effective workflow and improves user satisfaction. A manager can meet the target by controlling a project but sustainability is more versatile. Quality factors are the measuring criteria of a product while sustainability drives to make the quality product, efficient project, and successful organization so it is a package of strategy, tasks, processes, technologies, and stakeholders. It is observed that there is a lacking of sustainability practice in software engineering like other engineering communities. There are many software developing models that exist with limited scope in quality control for sustainability. Given the aforementioned viewpoint, this research proposes a new software project management framework, "SQ-Framework". Its hybrid structure consists of the features of methods, quality models, and sustainability. The execution guidance of "SQ-Framework" is provided according to "Karlskrona manifesto". A manager can use the framework to improve the management process of a project, a developer can integrate quality factors with sustainability into the product, an executive could be motivated to integrate quality and sustainability strategy in the organization, and the users get inspiration to practice sustainability.