A　growing　number　of　companies　deploy　their　applications　in　green　data　centers　(GDCs)　and　provide　services　to　tasks　of　global　users.　Currently,　a　growing　number　of　GDC　providers　aim　to　maximize　their　profit　by　deploying　green　energy　facilities　and　decreasing　brown　energy　consumption.　However,　the　temporal　variation　in　the　revenue,　price　of　grid,　and　green　energy　in　tasks＇　delay　bounds　makes　it　challenging　for　GDC　providers　to　achieve　profit　maximization　while　strictly　guaranteeing　delay　constraints　of　all　admitted　tasks.　Unlike　existing　studies,　a　time-aware　task　scheduling　(TATS)　algorithm　that　investigates　the　temporal　variation　and　schedules　all　admitted　tasks　to　execute　in　GDC　meeting　their　delay　bounds　is　proposed.　In　addition,　this　paper　provides　the　mathematical　modeling　of　task　refusal　and　service　rates.　In　each　iteration,　TATS　solves　the　formulated　profit　maximization　problem　by　hybrid　chaotic　particle　swarm　optimization　based　on　simulated　annealing.　Compared　with　several　existing　scheduling　algorithms,　TATS　can　increase　profit　and　throughput　without　violating　delay　constraints　of　all　admitted　tasks.