In this paper, the electronic transport characteristics of Fe/trans-polyacetylene/Fe magnetic tunnel junctions (MTJs) are investigated using multi-band tight-binding calculations within the framework of nonequilibrium Green function theory. A CH2 radical is added to different positions on the polymer chain and its effects on the tunnelling magnetoresistance of the MTJ are studied. The ferromagnetic electrodes are assumed to be single-band and their tight-binding parameters are chosen in such a way as to simulate the ab initio density functional calculations of the band structure of bcc-Fe along its [001] crystallographic direction. In building the Hamiltonian of the trans-polyacetylene (t-PA) chain, we have assumed an s orbital on the H atoms and one s and three p(px,py,pz) orbitals on the C atoms, and the dimerization effects are taken into account. It is found that moving the radical out of the centre of the polymer chain enhances the tunnelling magnetoresistance of the MTJ.