Scheduling　of　tasks　is　a　key　issue　in　the　grid　system.　The　solutions　space　of　the　sequences　of　the　independent　tasks　can　be　efficiently　searched　using　the　new　backtracking　algorithm　with　the　Max-Min　pruning　measures.　Compared　to　the　current　algorithms　such　as　Fast-Greedy,　Min-Min,　Max-Min　and　Max-Int,　the　new　backtracking　algorithm　can　get　the　optimal　completion　time　of　all　tasks.