We report the results of a first experimental search for lepton number violation by four units in the neutrinoless quadruple-β decay of ^{150}Nd using a total exposure of 0.19 kg yr recorded with the NEMO-3 detector at the Modane Underground Laboratory. We find no evidence of this decay and set lower limits on the half-life in the range T_{1/2}>(1.1-3.2)×10^{21} yr at the 90% C.L., depending on the model used for the kinematic distributions of the emitted electrons.