Global Software Development (GSD) is a well established field of software engineering with the benefits of a global environment. Software Project Management (SPM) plays a key role in the success of GSD. As a result, the need has arisen to study and evaluate the downsides of SPM for GSD, to thereby pave the way for the development of new methods, techniques, and tools with which to tackle them. This paper aims to identify and classify research on SPM approaches for GSD that are available in the literature, to identify their current weaknesses and strengths, and to analyze their applications in industry. We performed a Systematic Mapping Study (SMS) based on six classification criteria. Eighty-four papers were selected and analyzed. The results indicate that interest in SPM for GSD has been increasing since 2006. As a class of approaches, the most frequently reported methods (40%) are those used for coordination, planning, and monitoring, along with estimation techniques that can be used to better match a distributed project. SPM for GSD requires further investigation by researchers and practitioners, particularly with respect to cost and time estimations. These findings will help overcome the challenges that must to be considered in future SPM research for GSD, especially regarding collaboration and time-zone differences.