This　paper　develops　a　promising　alternative　for　solving　linear　quadratic(LQ)　optimal　control　problem　of　discrete-time　system,by　which　the　LQ　performance　index　is　transformed　into　the　energy　function　of　Boltzmann　machines,　and　the　control　sequence　into　the　state　vector　of　the　neurons　of　Boltzmann　machines.As　a　result,solving　LQ　dynamic　optimization　problem　is　equivalent　to　operating　associated　Boltzmann　machines　from　its　initial　state　to　the　terminal　state　that　represents　the　optimal　control　sequence.　The　theoretics　study　indicates　that　we　are　able　to　find　a　relevant　Boltzmann　machines　of　which　energy　function　is　corresponding　to　the　LQ　performance　index.　And　through　the　experimental　study　we　obtain　that　on　the　basis　of　this　method　we　proposed,　Boltzmann　machines　can　implement　linear　quadratic　optimal　control　of　any　multivariable　time-variant　system.