Broken spatial inversion symmetry in spin-orbital coupled systems leads to a mixing between orbitals with different parity, which results in unusual electronic structures and transport properties. We theoretically investigate the possibility of multipole ordering induced by a parity mixing. In particular, we focus on the system in which the parity mixing appears in a sublattice-dependent form. Starting from the periodic Anderson model with such a local parity mixing, we derive an extended Kondo lattice model with sublattice-dependent antisymmetric exchange couplings between itinerant electrons and localized spins. By variational calculation, simulated annealing, and Monte Carlo simulation, we show that the model on a quasi-one-dimensional zigzag lattice exhibits an odd-parity multipole order composed of magnetic toroidal and quadrupole components at and near half-filling. The multipole order causes a band deformation with the band bottom shift and a magnetoelectric response. The results suggest that unusual odd-parity multipole orders will be widely observed in multiorbital systems with local parity mixing.