Low-mass population III (PopIII) stars of $lesssim 0.8 M_{odot}$ could survive up until the present. Non-detection of low-mass PopIII stars in our Galaxy has already put a stringent constraint on the initial mass function (IMF) of PopIII stars, suggesting that PopIII stars have a top-heavy IMF. On the other hand, some claims that the lack of such stars stems from 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. The stellar wind and radiation of low-mass PopIII stars are modeled based on knowledge of nearby low-mass stellar systems including our Sun. 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. Especially, the accretion abundance of iron will be reduced by a factor of $< 10^{-12}$ compared with Bondi-Hoyle-Lyttleton accretion. The metal accretion can enhance iron abundance [Fe/H] only up to $sim -14$. 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.
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