In　this　paper,　we　consider　numerical　approximations　for　a　model　of　smectic-A　liquid　crystal　flows　in　its　weak　flow　limit.　The　model,　derived　from　the　variational　approach　of　the　de　Gennes　free　energy,　is　consisted　of　a　highly　nonlinear　system　that　couples　the　incompressible　Navier-Stokes　equations　with　two　nonlinear　order　parameter　equations.　Based　on　some　subtle　explicit-implicit　treatments　for　nonlinear　terms,　we　develop　an　unconditionally　energy　stable,　linear　and　decoupled　time　marching　numerical　scheme　for　the　reduced　model　in　the　weak　flow　limit.　We　also　rigorously　prove　that　the　numerical　scheme　obeys　the　energy　dissipation　law　at　the　discrete　level.　Various　numerical　simulations　are　presented　to　demonstrate　the　accuracy　and　the　stability　of　the　scheme.