We present the full NLO SUSY-QCD corrections to the pair production of neutralinos and charginos at the LHC in association with a jet and their matching to parton-shower programs in the framework of the POWHEG-BOX package. The code we have developed provides a SUSY Les Houches Accord interface for setting electroweak and supersymmetric input parameters. Decays of the neutralinos and charginos and parton-shower effects can be simulated with multi-purpose programs such as PYTHIA. The capabilities of the code are illustrated by phenomenological results for a parameter point in the framework of pMSSM10, compatible with present experimental limits on supersymmetry. We find that NLO-QCD corrections as well as parton-shower effects are of primary importance for the appropriate description of jet distributions.