In　this　paper,　we　consider　the　dynamic　k-level　facility　location　problem,　which　is　a　generalization　of　the　uncapacitated　k-level　facility　location　problem　when　considering　time　factor.　We　present　a　combinatorial　primal-dual　approximation　algorithm　for　the　problem　which　finds　a　solution　within　6　times　the　optimum.　This　approximation　ratio　under　a　dynamic　setting　coincides　with　that　of　the　simple　dual　ascent　6-approximation　algorithm　for　the　(static)　multilevel　facility　location　problem　(Bumb,　2001)　with　a　weak　triangle　inequality　property.