Littlest Higgs model and associated ZH production at high energy $e^{+}{e}^{-}$ collider

In the context of the littlest Higgs (LH) model, we consider the Higgs strahlung process $e^{+}{e}^{-}\to ZH$. We find that the correction effects on this process mainly come from the heavy photon $B^{\mathrm{\prime }}$. If we take the mixing angle parameter $c$ in the range of 0.75 - 1, the contributions of the heavy gauge boson $W_3^{\mathrm{\prime }}$ is larger than 6%. In most of the parameter space, the deviation of the total production cross section ${\sigma }^{tot}$ from its SM value is larger than 5%, which may be detected in the future high energy $e^{+}{e}^{-}$ collider (LC) experiments. The future LC experiments could test the LH model by measuring the cross section of the process $e^{+}{e}^{-}\to ZH$.