  In the littlest Higgs model with T-parity (LHT), the mirror quarks have
flavor structures and will contribute to the top quark flavor changing neutral
current. In this work, we perform an extensive investigation of the top quark
rare three-body decays $t\to cVV (V=\gamma,Z,g)$ and $t\to cf\bar{f}
(f=b,\tau,\mu,e)$ at one-loop level. Our results show that the branching ratios
of $t\to cgg$ and $t\to cb\bar{b}$ could reach $\mathcal {O}(10^{-3})$ in the
favorite parameter space of the littlest Higgs model with T-parity, which
implies that these decays may be detectable at the LHC or ILC, while for the
other decays, their rates are too small to be observable at the present or
future colliders.
