The　optimal　control　problem　of　the　switched　system　which　subsystem　is　discrete　linear　system　is　investigated.　At　the　condition　of　the　given　switched　number,　and　the　quadratic　performance　function,　the　multi-periods　decision-making　problem　can　be　transformed　into　single　decision-making　problem　to　resolve,　then　the　analytic　solution　of　the　switched　discrete　system　optimal　control　problem　can　obtained　in　global.　Searching　of　the　switched　instant　and　sequence　to　minimum　the　performance　function　by　genetic　algorithm,　and　the　searching　procedure　is　presented.　A　numerical　example　illustrates　the　effectiveness　of　the　design　approach.　The　simulation　shows　that　the　approach　can　resolve　a　kind　of　switched　discrete　optimal　control　problem.