Driven　by　the　rapid　development　of　modern　industrial　processes,　cyber-physical　systems　(CPSs),　which　tightly　conjoin　computational　and　physical　resources,　have　become　ever-more　prevalent　during　recent　years.　However,　due　to　the　intrinsical　vulnerability　of　the　cyber　layer,　the　system　performances　of　CPSs　are　easily　degraded　by　malicious　false　data　injection　(FDI)　attacks,　which　are　launched　by　adversary.　In　this　article,　the　issue　of　secure　reconstruction　is　considered　for　linear　CPSs　with　simultaneous　sparse　actuator　and　sensor　attacks.　First,　an　adaptive　counteraction　searching　strategy　is　proposed　to　identify　the　potential　combinational　attack　mode.　In　this　way,　malicious　FDI　attacks　are　excluded.　Second,　by　constructing　a　descriptor　switched　sliding　mode　observer,　the　sparse　FDI　attacks　and　the　system　state　are　reconstructed　effectively.　Meanwhile,　sufficient　conditions　of　the　error　convergence　can　be　derived.　Finally,　a　numerical　simulation　is　utilized　to　illustrate　the　applicability　of　the　proposed　theoretical　derivation.