  The structure and magnetic properties of rare-earth ions Tm$^{3+}$ kagom\'{e}
lattice Tm$_3$Sb$_3$Mg$_2$O$_{14}$ are studied by X-ray diffraction, magnetic
susceptibility and muon spin relaxation ($\mu$SR) experiments. The existence of
a small amount of Tm/Mg site-mixing disorder is revealed. DC magnetic
susceptibility measurement shows that Tm$^{3+}$ magnetic moments are
antiferromagnetically correlated with a negative Curie-Weiss temperature of
-26.3 K. Neither long-range magnetic order nor spin-glass transition is
observed by DC and AC magnetic susceptibility, and confirmed by $\mu$SR
experiment down to 0.1 K. However, the emergence of short-range magnetic order
is indicated by the zero-field $\mu$SR experiments, and the absence of spin
dynamics at low temperatures is evidenced by the longitudinal-field $\mu$SR
technique. Compared with the results of Tm$_3$Sb$_3$Zn$_2$O$_{14}$, another
Tm-based kagom\'{e} lattice with much more site-mixing disorder, the gapless
spin liquid like behaviors in Tm$_3$Sb$_3$Zn$_2$O$_{14}$ can be induced by
disorder effect. Samples with perfect geometrical frustration are in urgent
demand to establish whether QSL exits in this kind of materials with rare-earth
kagom\'{e} lattice.
