The aggregate throughput of wireless mesh networks (WMNs) can be significantly improved by equipping the mesh routers with multiple radios tuned to orthogonal channels. Not only the links using orthogonal channels can be activated at a time, but some links in the same channel also can be activated concurrently if the Signal-to-Interference-and-Noise Ratio (SINR) at their receivers is not lower than the threshold, which is the spatial-reuse characteristic. STDMA is considered as one of the medium access schemes that can exploit spatial reuse to improve network throughput. Past studies have shown that optimizing the performance of STDMA is NP-Hard. Therefore, we propose a STDMA-based scheduling algorithm that operates in a greedy fashion for WMNs. We show that the proposed algorithm enhances not only the throughput but also the fairness by capturing the essence of spatial-reuse approach of STDMA and giving medium access opportunities to each network element based on its priority. We furthermore validate our algorithm through theoretical analysis and extensive simulations and the results show that our algorithm can outperform state-of-the-art alternatives.