Voice conversion (VC) based on Gaussian mixture model (GMM) is the most classic and common method which converts the source spectrum to target spectrum.However this method is prone to over-fitting because of its frame-by-frame conversion.The VC with non-negative matrix factorization (NMF) is presented in this paper,which can keep spectrum from over-fitting by adjusting the size of basis vector (dictionary).In order to realize the non-linear mapping better,kernel NMF (KNMF) is adopted to achieve spectrum mapping.In addition,to increase the accuracy of conversion,KNMF combined with GMM (GKNMF) is also introduced into VC.In the end,KNMF,GKNMF,GMM,principal component regression (PCR),PCR combined with GMM (GPCR),partial least square regression (PLSR),NMF correlation-based frequency warping (NMF-CFW) and deep neural network (DNN) methods are compared with each other.The proposed GKNMF gets better performance in both objective evaluation and subjective evaluation.