We study the left-right asymmetric model based on SU(3)_C \otimes SU(2)_L \otimes SU(3)_R \otimes U(1)_X gauge group, which improves the theoretical and phenomenological aspects of the known left-right symmetric model. This new gauge symmetry yields that the fermion generation number is three, and the tree-level flavor-changing neutral currents arise in both gauge and scalar sectors. Also, it can provide the observed neutrino masses as well as dark matter automatically. Further, we investigate the mass spectrum of the gauge and scalar fields. All the gauge interactions of the fermions and scalars are derived. We examine the tree-level contributions of the new neutral vector, Z'_R, and new neutral scalar, H_2, to flavor-violating neutral meson mixings, say K-\bar{K}, B_d-\bar{B}_d, and B_s-\bar{B}_s, which strongly constrain the new physics scale as well as the elements of the right-handed quark mixing matrices. The bounds for the new physics scale are in agreement with those coming from the \rho-parameter as well as the mixing parameters between W, Z bosons and new gauge bosons.