Non-negative Matrix Factorization (NMF) algorithm can only be used to find low rank approximation of original non-negative data while Concept Factorization (CF) algorithm extends matrix factorization to single non-linear kernel space, improving learning ability and adaptability of matrix factorization. In unsupervised environment, to design or select proper kernel function for specific dataset, a new algorithm called Globalized Multiple Kernel CF (GMKCF) was proposed. Multiple candidate kernel functions were input in the same time and learned in the CF framework based on global linear fusion, obtaining a clustering result with high quality and stability and solving the problem of kernel function selection that the CF faced. The convergence of the proposed algorithm was verified by solving the model with alternate iteration. The experimental results on several real databases show that the proposed algorithm outperforms comparison algorithms in data clustering, such as Kernel K-Means (KKM), Spectral Clustering (SC), Kernel CF (KCF), Co-regularized multi-view spectral clustering (Coreg), and Robust Multiple KKM (RMKKM).