With the number of cyber-attacks growing rapidly and the opportunities to attack companies widening, vulnerability management is gaining increased importance. It needs to reduce the variety of possibilities by remediating vulnerabilities found in IT infrastructures. Process mining is an established method used to discover, analyze, and manage data on (implemented) business processes. This paper proposes utilizing process mining for business-critical processes, including IT processes. This work explores how vulnerability management processes can be improved through process monitoring, targeting the operation time of processes, remediation, and the continuous management of the vulnerability process design. Thereby, process mining is applied for monitoring following the CRISP data mining approach. Process analysis includes process discovery, conformance checking, and process enhancement. Improving the vulnerability management process is based on the discovered vulnerability process, which is enhanced with throughput time data as well as priority, source, and assignment group data. Improvements concern changing the configuration of a source and better training for certain assignment groups. Process discovery can also be used to identify the cause for improper remediation of vulnerabilities. In this case, unwanted activity flows, which indicate that a major part of the vulnerability management process is being skipped, need to be identified. Finally, the continuous use of process mining allows for the monitoring of process modifications, including the impact of implemented improvements.