The nature of pulsars is still unknown because of the non-perturbative effects of the fundamental strong interaction,so various models of pulsar inner structures are suggested,either for conventional neutron stars or quark stars.Additionally,a quark-cluster matter state is conjectured for cold matter at supranuclear density,and as a result pulsars can be quark-cluster stars.Besides understanding the different manifestations,the most important issue is to find an effective way to observationally differentiate these models.X-ray polarimetry plays an important role here.The thermal x-ray polarization of quark/quark-cluster stars is focused on,and while the thermal x-ray linear polarization percentage is typically higher than ～10％ in normal neutron star models,the percentage of quark/quark-cluster stars is almost zero.This could then be an effective method to identify quark/quark-cluster stars by soft x-ray polarimetry.We are therefore expecting to detect thermal x-ray polarization in the coming decades.