We propose a novel heterogeneous scalable desktop grid system, WaveGrid, which uses a peer-to-peer architecture and can satisfy the needs of applications with fastturnaround requirements. In WaveGrid, hosts self-organize into a timezone-aware overlay network, which supports straightforward, quick resource discovery. Scheduling methods in WaveGrid take heterogeneity into account in selecting scheduling and migration targets. WaveGrid then rides the wave of available cycles by migrating jobs to hosts located in idle night-time zones around the globe. We evaluate WaveGrid using a heterogeneous host CPU power profile based on empirical data collected from the global computing project BOINC. The simulation results show that WaveGrid perform consistently well with fast turnaround time and low migration overhead. It performs much better than other systems with respect to turnaround, stability and minimal impacts on hosts.