The　slow　development　of　traditional　computing　has　prompted　the　search　for　new　materials　to　replace　silicon-based　computers.　Bio-computers,　which　use　molecules　as　the　basis　of　computation,　are　highly　parallel　and　information　capable,　attracting　a　lot　of　attention.　In　this　study,　we　designed　a　NAND　logic　gate　based　on　the　DNA　strand　displacement　mechanism.　We　assembled　a　molecular　calculation　model,　a　4-wire-2-wire　priority　encoder　logic　circuit,　by　cascading　the　proposed　NAND　gates.　Different　concentrations　of　input　DNA　chains　were　added　into　the　system,　resulting　in　corresponding　output,　through　DNA　hybridization　and　strand　displacement.　Therefore,　it　achieved　the　function　of　a　priority　encoder.　Simulation　results　verify　the　effectiveness　and　accuracy　of　the　molecular　NAND　logic　gate　and　the　priority　coding　system　presented　in　this　study.　The　unique　point　of　this　proposed　circuit　is　that　we　cascaded　only　one　kind　of　logic　gate,　which　provides　a　beneficial　exploration　for　the　subsequent　development　of　complex　DNA　cascade　circuits　and　the　realization　of　the　logical　coding　function　of　information.