  The littlest Higgs (LH) model predicts the existence of the new gauge bosons
$Z'$ and $B'$. We calculate the contributions of these new particles to the
processes $e^{+}e^{-}\to\bar{f}f$ with $f=\tau, \mu, b,$ or $c$ and study the
possibility of detecting these new particles via these processes in the future
high-energy linear $e^{+}e^{-}$ collider (LC) experiments with
$\sqrt{s}=500GeV$ and $\pounds_{int}=340fb^{-1}$. We find that, with reasonable
values of the parameter preferred by the electroweak precision data, the
possible signals of these new particles might be detected. The $Z'$ mass
$M_{Z'}$ can be explored up to $2.8TeV$ via the process $e^{+}e^{-}\to\bar{b}b
$ for $0.3\leq c \leq 0.5 $ and the $B'$ mass $M_{B'}$ can be explored up to
$1.26TeV$ via the process $e^{+}e^{-}\to\bar{l}l $ for $0.64\leq c' \leq 0.73
$.
