The　selection　of　the　shortest　path　problem　is　one　of　the　classic　problems　in　the　graph　theory.　The　relationship　between　objects　in　a　complex　environment　usually　has　fuzziness,　hesitancy,　uncertainty　and　inconsistency.　A　neutrosophic　set　is　characterized　by　the　degree　of　truth-membership,　indeterminacy-membership　and　falsity-membership,　and　is　more　capable　of　capturing　incomplete　information.　The　selection　of　the　shortest　path　of　the　neutrosophic　graph　based　on　the　theory　of　neutrosophic　set　and　graph　theory　has　become　a　key　issue.　For　the　shortest　path　problem　in　the　neutrosophic　graph,　in　which　the　edge　length　is　assigned　a　trapezoidal　fuzzy　neutrosophic　number　instead　of　a　real　number,　a　solving　method　based　on　the　extended　dynamic　programming　is　proposed.　The　path　length　is　compared　using　the　score　function　and　the　accuracy　function　based　on　the　trapezoidal　fuzzy　neutrosophic　numbers.　An　extended　dynamic　programming　method　for　solving　the　shortest　path　problem　is　presented　to　obtain　the　shortest　path　and　the　shortest　path　length.　Finally,　two　examples　are　used　to　verify　the　feasibility　of　this　method,　and　the　comparison　and　analysis　with　the　Dijkstra　algorithm　illustrate　the　rationality　and　effectiveness　of　this　method.　And　the　impact　of　using　different　sorting　methods　on　the　selection　of　the　shortest　path　of　the　neutrosophic　graph　is　analyzed.　©　2019,　Editorial　Office　of　Control　and　Decision.　All　right　reserved.