Based on a π-orbital tight-binding model Hamiltonian and the Green’s function approach together with the Landauer formalism, we studied the coherent spin-dependent transport properties of ferromagnetic (FM)-molecule-FM junctions for the molecule to be trans-polyacetylene (t-PA). The conductance properties of the spin system are studied for a t-PA molecule of fixed length. It is shown that tunnel magnetoresistance (TMR) of the molecular junction can be quite large (over 60%) and the TMR value depends on applied voltage. The TMR maximum value for a t-PA junction is obtained at a low applied voltage (Va<0.7).