Nonnegative tensor factorization (NTF) is a recent multiway (multilinear) extension of negative matrix factorization (NMF), where nonnegativity constraints are mainly imposed on CANDECOMP/PARAFAC model and recently, also, on Tucker model. Nonnegative tensor factorization algorithms have many potential applications, including multiway clustering, multi-sensory or multidimensional data analysis and nonnegative neural sparse coding. In this paper we will present new approach to NTF which is based on CANDENCOMP/PARAFAC model. The proposed method is simple, computationally effective, easily extensible to higher dimensional tensors, can handle some problems related to rank-deficient tensors and can be used for analysis of the higher dimensional tensors than most of the known algorithms for NTF.