We report multi-epoch, simultaneous 22 GHz water and 44 GHz Class I methanol maser line survey towards 180 intermediate-mass young stellar objects, including 14 Class 0, 19 Class I objects, and 147 Herbig Ae/Be stars. We detected $H_2O$ and $CH_3OH$ maser emission towards 16 (9%) and 10 (6%) sources with one new $H_2O$ and six new $CH_3OH$ maser sources. The detection rates of both masers rapidly decrease as the central (proto)stars evolve, which is contrary to the trends in high-mass star-forming regions. This suggests that the excitations of the two masers are closely related to the evolutionary stage of the central (proto)stars and the circumstellar environments. $H_2O$ maser velocities deviate on average 9 km s-1 from the ambient gas velocities whereas $CH_3OH$ maser velocities well match with. For both maser emissions, large velocity difference (${mid}v_{H2O}-v_{sys}{mid};>; 10kms^{-1}; and;{mid}v_{CH3OH}-v_{sys}{mid};>;1kms^{-1}$) is mostly confined to Class 0 objects. The formation and disappearance of $H_2O$ maser lines are frequent and the integrated intensities of them change up to two orders of magnitude. In contrast, $CH_3OH$ maser lines usually show no significant change in the intensity, shape, and velocity. This consistent with the previous suggestion that $H_2O$ maser emission originates from the base of an outflow while 44 GHz Class I $CH_3OH$ maser emission arises from the interaction region of the outflow with the ambient gas. The isotropic maser luminosities are well correlated with the bolometric luminosities of the central the objects. The fitted relations are $L_{H2O}=1.71{ast}10^{-9}(L_{bol})^{0.97}$ and $L_{CH3OH}=1.71{ast}10^{-10}(L_{bol})^{1.22}$.