Reconfigurable computing has become an important part of research in software systems and computer architecture. While prior research on reconfigurable computing have addressed architectural and compilation/programming aspects to some extent, there is still not much consensus on what kind of operating system (OS) support should be provided. In this paper, we focus on OS process scheduler, and demonstrate how it can be customized considering the needs of reconfigurable hardware. Our process scheduler is configuration sensitive, that is, it reuses the current FPGA configuration as much as possible. Our extensive experimental results show that the proposed scheduler is superior to classical scheduling algorithms such First-Come-First-Serve (FCFS) and Shortest Job First (SJF).