We report the results of a first experimental search for lepton number violation by four units in the neutrinoless quadruple-beta decay of Nd-150 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) x 10(21) yr at the 90% C.L., depending on the model used for the kinematic distributions of the emitted electrons.