We present a systematic theoretical investigation on the work functions of five closed surfaces of metal hexaborides including LaB6, BaB6, CaB6, CeB6, SrB6 and SmB6. The results are in a close agreement with available experimental measurements and previous theoretical findings. The variations of the work function display a good trend. For BaB6, CaB6 and SrB6, the increasing order is (100) (110) (211) (112) (111). For CeB6, LaB6, and SmB6, the sequence is somewhat different: (100) (211) (112) (110) (111). The work function changes with the metal hexaborides series have also been discussed. The increasing order of the (100) surface is LaB6(100) CeB6(100) SmB6(100) SrB6(100) BaB6(100) CaB6(100). The orders for the (110) and (111) surface are similar: BaB6(110, 111) SrB6(110, 111) LaB6(110, 111) CeB6(110, 111) CaB6(110, 111) SmB6(110, 111). For the (112) and (211) surface, the sequence is BaB6(112, 211) LaB6(112, 211) CeB6(112, 211) SrB6(112, 211) SmB6(112, 211) CaB6(112, 211). [ABSTRACT FROM AUTHOR]