Project portfolio management (PPM) is considered a central part for achieving intended strategies for organisations. However, only a percentage of strategies are actually realised, and whilst much previous research has focused on the formulation of strategies, less has been directed towards the realisation. To gain further understanding of how PPM can contribute to realising strategies, this thesis studied the PPM activities of selecting projects and allocating resources, and related challenges when trying to achieve a strategically aligned project portfolio in a matrix organisation. A qualitative case study was performed at a pharmaceutical production company in Stockholm referred to as Medex. An abductive research approach was used, and the data was thematically analysed whilst striving to achieve triangulation. The study was divided into a pre-study and a main study consisting of a total of 15 semi-structured interviews with participants at different positions within the organisation, in parallel to the collection of secondary data from Medex’s intranet.    The study indicate that it is a challenge for a matrix organisation to align projects to strategy through project objectives, and that it is rather project values’ strong connection to strategy that provide a clear link between projects and strategy. It further suggests that using project value for linking projects to strategy can increase the understanding of the motivation of project priorities, as well as creating a foundation for determining if the allocation of resources is oriented towards strategy. Furthermore, the study demonstrates the challenge and necessity for top management to base their decisions on sufficient and reliable information. Moreover, the selection of projects must be performed in accordance with available resource capacity, which highlights the need for strong connections between short-, medium- and long-term resource allocation. Furthermore, the study emphasises the need for a structured way of evaluating PPM processes to improve and address associated challenges. Additionally, the high competition between resources in a matrix organisation is depicted and the study indicates that a strong focus on profits can limit the possibility of achieving a strategically aligned project portfolio. While the study is based on a single case, the findings can be regarded as transferable, at varying extents, to other companies of similar size and organisational structure as well.