Quantum computers can approximately prepare the ground states of many physical systems without using an exponential amount of resources. A hybrid quantum-classical algorithm, such as the variational quantum eigensolver (VQE), is a promising candidate for simulating electronic structures on a near-term device. Simulating complex systems with VQE, however, poses serious challenges because of limited qubit coherence times and non-negligible error rates within near-term devices. To tackle this challenge, we integrate the geometric structure of Deep Multiscale Entanglement Renormalization Ansatz (DMERA) circuits with the low-cost error mitigation, using fermionic parity symmetry verification, to simulate ground states of the Fermi-Hubbard model and the jellium model. Requiring only a gate depth logarithmic in the total system size and a number of qubits independent of the system size, this protocol enables us to study larger systems than are possible for approaches with different ansatzes. Results for the Fermi-Hubbard model and the jellium model indicate that the DMERA protocol, combined with the error mitigation, effectively leverages the ability of near-term devices to simulate complex lattice models.