We present the result of an indirect search for high energy neutrinos from WIMP annihilation in the Sun using upward-going muon (upmu) events at Super-Kamiokande. Datasets from SKI-SKIII (3109.6 days) were used for the analysis. We looked for an excess of neutrino signal from the Sun as compared with the expected atmospheric neutrino background in three upmu categories: stopping, non-showering, and showering. No significant excess was observed. The 90% C.L. upper limits of upward-going muon flux induced by WIMPs of 100 GeV/c$^2$ were 6.4$times10^{-15}$ cm$^{-2}$ sec$^{-1}$ and 4.0$times10^{-15}$ cm$^{-2}$ sec$^{-1}$ for the soft and hard annihilation channels, respectively. These limits correspond to upper limits of 4.5$times10^{-39}$ cm$^{-2}$ and 2.7$times10^{-40}$ cm$^{-2}$ for spin-dependent WIMP-nucleon scattering cross sections in the soft and hard annihilation channels, respectively.
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