One　of　challenging　issues　for　task　allocation　problem　in　wireless　sensor　networks　(WSNs)　is　distributing　sensing　tasks　rationally　among　sensor　nodes　to　reduce　overall　power　consumption　and　ensure　these　tasks　finished　before　deadlines.　In　this　paper,　we　propose　a　soft　real-time　fault-tolerant　task　allocation　algorithm　(FTAOA)　for　WSNs　in　using　primary/backup　(P/B)　technique　to　support　fault　tolerance　mechanism.　In　the　proposed　algorithm,　the　construction　process　of　discrete　particle　swarm　optimization　(DPSO)　is　achieved　through　adopting　a　binary　matrix　encoding　form,　minimizing　tasks　execution　time,　saving　node　energy　cost,　balancing　network　load,　and　defining　a　fitness　function　for　improving　scheduling　effectiveness　and　system　reliability.　Furthermore,　FTAOA　employs　passive　backup　copies　overlapping　technology　and　is　capable　to　determinate　the　mode　of　backup　copies　adaptively　through　scheduling　primary　copies　as　early　as　possible　and　backup　copies　as　late　as　possible.　To　improve　resource　utilization,　we　allocate　tasks　to　the　nodes　with　high　performance　in　terms　of　load,　energy　consumption,　and　failure　ratio.　Analysis　and　simulation　results　show　the　feasibility　and　effectiveness　of　FTAOA.　FTAOA　can　strike　a　good　balance　between　local　solution　and　global　exploration　and　achieve　a　satisfactory　result　within　a　short　period　of　time.