Asset management has become an active field of research with the consolidation of the international ISO 55000 series. It coordinates activities to realize value from assets in organizations. Maintenance is one of the main stages to deliver business outcomes from physical assets over its life cycle. In the fourth industrial revolution scenario, it could not be different. Establishing activities to address unwanted incidents, nonconformities, and opportunities for improvement is an important and required element in the maintenance management of an asset management system. The standards, however, are not specific and only determine what needs to be done, not how to do it. Accordingly, this paper proposes a framework for maintenance management improvement (MMI) based on the international standard ISO 55000 series for asset management. To this end, a four-step methodology was applied. First, an ISO 55000 series review focused on a broad understanding of the concepts and requirements for the improvements in an asset management system is presented. Then, a framework was developed for MMI and demonstrated through a maintenance case study application in a Brazilian hydroelectric plant. Finally, the framework processes were correlated and discussed with the improvement requirements of ISO 55001. As the main result, an MMI framework for addressing improvements has been demonstrated to maintenance management for asset management. It encompasses activities for elaborating control and corrective actions, dealing with consequences, addressing opportunities for improvement, critically assessing events, and analyzing root causes. It was evidenced the framework is able to address nonconformities, incidents, and opportunities systematically. Therefore, these findings are expected to contribute to the researchers and practitioners in the field of asset management as the proposed framework based on the ISO 55000 series is an approach to the achievement of continuous improvement in maintenance management and, consequently, in asset management.