In recent years, nonlinear unmixing of hyperspectral data has become an attractive topic in hyperspectral image analysis, because nonlinear models appear as more appropriate to represent photon interactions in real scenes. For this challenging problem, nonlinear methods operating in reproducing kernel Hilbert spaces have shown particular advantages. In this paper, we derive an efficient nonlinear unmixing algorithm based on a recently proposed linear mixture/ nonlinear fluctuation model. A multi-kernel learning support vector regressor is established to determine material abundances and nonlinear fluctuations. Moreover, a low complexity locally-spatial regularizer is incorporated to enhance the unmixing performance. Experiments with synthetic and real data illustrate the effectiveness of the proposed method.