The Large High Altitude Air Shower Observatory (LHAASO) is a next-generation observatory for high energy gamma rays and cosmic rays with wide field of view. It will detect gamma rays with high sensitivity in the energy range from 300 GeV to 1 PeV. Therefore, it is promising for LHAASO to search for the high-energy gamma rays induced by dark matter (DM) self-annihilation in dwarf spheroidal satellite galaxies (dSphs), which are ideal objects for the DM indirect detection. In this work, we investigate the LHAASO sensitivity to DM self-annihilation signatures for 19 dSphs and take the uncertainties on the spatial DM distribution of dSphs into account. We perform a joint likelihood analysis for the 19 dSphs and find that the LHAASO sensitivity to the DM annihilation cross section will reach $mathcal{O}(10^{-24})sim mathcal{O}(10^{-25})$ cm$^3$ s$^{-1}$ at the mass scale above TeV for several annihilation modes, which is larger than the canonical thermal relic cross section by a factor of 10 to 100.
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