X-ray-dim isolated neutron stars (XDINSs) are characterized by Planckian spectra in X-ray bands, but show optical/ultraviolet (UV) excesses: the factors by which the measured photometry exceeds those extrapolated from X-ray spectra. To solve this problem, a radiative model of bremsstrahlung emission from a plasma atmosphere is established in the regime of a strangeon star. A strangeon star atmosphere could simply be regarded as the upper layer of a normal neutron star. This plasma atmosphere, formed and maintained by the interstellar-medium-accreted matter due to the so-called strangeness barrier, is supposed to be of two temperatures. All seven XDINS spectra could be well fitted by the radiative model, from optical/UV to X-ray bands. The fitted radiation radii of XDINSs are from 7 to 13 km, while the modeled electron temperatures are between 50 and 250 eV, except RX J0806.4-4123, with a radiation radius of similar to 3.5 km, indicating that this source could be a low-mass strangeon star candidate. This strangeon star model could further be tested by soft X-ray polarimetry, such as the Lightweight Asymmetry and Magnetism Probe, which is expected to be operational on China's space station around 2020.