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We report the thermodynamic and muon spin relaxation (μSR) evidences for a possible gapless spin liquid in Tm₃Sb₃Zn₂O₁₄, with the rare-earth ions Tm³⁺ forming a two-dimensional kagome lattice. We extract the magnetic specific heat of Tm₃Sb₃Zn₂O₁₄ by subtracting the phonon contribution of the non-magnetic isostructural material La₃Sb₃Zn₂O₁₄ and obtain a clear linear-T temperature dependence of magnetic specific heat at low temperatures. The absence of magnetic order is confirmed by specific heat, A.C. susceptibility and μSR measurements down to 20 mK. We find that the spin-lattice relaxation time remains constant down to the lowest temperature. The possibility of disorder induced effect could not be excluded duo to the possible Tm/Zn site-mixing disorder in Tm₃Sb₃Zn₂O₁₄.