Software process metrics are being used for improving agile processes in software companies. This helps a lot in managing customer satisfaction and the growth of the company. Different studies have stated different process metrics and practitioners are using various metrics in terms of software process improvement. However, it is difficult to find out the best-suited metrics for every company as per the project nature. A systematic mapping study is used to identify potential process improvement metrics and finding the best metrics in agile development. We have found only 13 papers on process metrics. Finally, we have classified them into three categories assuming their impacting factors. This study provides an overview of agile software development process metrics that will help the practitioners to adopt efficient process metrics in Global Software Development (GSD).