We present an implementation of the next-to-leading order vector boson plus one jet production process in hadronic collision in the framework of POWHEG, which is a method to implement NLO calculations within a Shower Monte Carlo context. All spin correlations in the vector boson decay products have been taken into account. The process has been implemented in the framework of the POWHEG-BOX, an automated computer code for turning a NLO calculation into a shower Monte Carlo program. We present phenomenological results for the case of the Z/gamma plus one jet production process, obtained by matching the POWHEG calculation with the shower performed by PYTHIA, for the LHC, and we compare our results with available Tevatron data.