In　order　to　solve　linear　quadratic　(LQ)　optimal　control　problem　of　discrete-time　system,　the　authors　present　a　promising　alternative　based　on　random　neural　network-Boltzmann　machines.　By　the　method,　the　LQ　performance　index　is　transformed　into　the　energy　function　of　Boltzmann　machine,　and　the　control　sequence　is　transformed　into　the　neuron　state　vector　of　Boltzmann　machines.　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　theoretical　study　indicates　that　we　are　able　to　find　a　relevant　Boltzmann　machines　whose　energy　function　is　corresponding　to　the　LQ　performance　index.　Emulation　experiment　shows　Boltzmann　machines　can　implement　linear　quadratic　optimal　control　of　any　multivariable　time-variant　system.