Low-mass population III (PopIII) stars could survive up until the present. They would be found in the halo of Our Galaxy, if they exist. Non-detection of low-mass PopIII stars in our Galaxy suggests that PopIII stars have a top-heavy IMF. On the other hand, some claims that the lack of such stars is as a result of metal enrichment of their surface by accretion of heavy elements from interstellar medium (ISM). We investigate effects of the stellar wind on the metal accretion onto low-mass PopIII stars because accretion of the local ISM onto the Sun is prevented by the solar wind even for neutrals. We find that low-mass PopIII stars traveling across the Galaxy forms the stellar magnetosphere in most of their life. Once the magnetosphere is formed, most of neutral interstellar particles are photoionized before reaching to the stellar surface and are blown away by the wind. This demonstrates that low-mass PopIII stars remain pristine and will be found as metal free stars and that further searches for them are valuable to constrain the IMF of PopIII stars.