Big data refers to large complex structured or unstructured data sets. Big data technologies enable organisations to generate, collect, manage, analyse, and visualise big data sets, and provide insights to inform diagnosis, prediction, or other decision-making tasks. One of the critical concerns in handling big data is the adoption of appropriate big data governance frameworks to (1) curate big data in a required manner to support quality data access for effective machine learning and (2) ensure the framework regulates the storage and processing of the data from providers and users in a trustworthy way within the related regulatory frameworks (both legally and ethically). This paper proposes a framework of big data governance that guides organisations to make better data-informed business decisions within the related regularity framework, with close attention paid to data security, privacy, and accessibility. In order to demonstrate this process, the work also presents an example implementation of the framework based on the case study of big data governance in cybersecurity. This framework has the potential to guide the management of big data in different organisations for information sharing and cooperative decision-making.