The coherent quantum transport properties through the spin-polarized polyphenoxyl radical molecule have been investigated, using the density-functional-derived tight-binding model and the Green's functions method. The majority and minority spin components exhibit considerably different transmission spectra in the vicinity of the Fermi level. Namely, each spin component carries a different amount of current when the bias voltage is applied between the two electrodes that sandwich the polyradical molecule. Therefore, if the magnetization axis of the polyradical is fixed by the external magnetic field, and if the spin flip does not occur during the transmission, the assumed molecular bridge is expected to work as a spin filter or a spin valve. Furthermore, as long as the bias voltage is weak, the total spin current is observed to be larger than the current through its reduced molecular form. It indicates that the adsorption of some chemical species on the radical sites can be sensed by the change in conductance of the molecular bridge.