We introduce a hybrid quantum-classical algorithm to compute the Green function for strongly correlated electrons on noisy intermediate-scale quantum (NISQ) devices. The technique consists in the construction of a non-orthogonal excitation basis composed of a set of single-particle excitations generated by occupation number operators. The excited sectors of the Hamiltonian in this basis can then be measured on the quantum device and a classical post-processing procedure yields the Green function in the Lehmann representation. The technique allows for noise filtering, a useful feature for NISQ devices. To validate the approach, we carry out a set of proof-of-principle calculations on the single-band Hubbard model on IBM quantum hardware. For a 2 site system we find good agreement between the results of quantum simulations and the exact result for the local spectral function. This proof-of-principle also shows that the noise filtering provides a reliable way to get rid of satellite peaks present in the spectral weight obtained from a NISQ device. A simulation of a 4 site system carried out on classical hardware suggests that the approach can achieve similar accuracy for larger systems.