This article presents a novel supervised target detection approach on hyperspectral images based on Fukunaga-Koontz Transform (FKT) with compositional kernel combination. The Fukunaga-Koontz Transform is one of the most effective techniques for solving problems that involve two-pattern characteristics. To capture nonlinear properties of data, researchers have extended FKT to kernel FKT (KFKT) by means of kernel machines. However, the performance of KFKT depends on choosing convenient kernel functions and/or selection of the proper parameter(s). In this work, instead of selecting a single kernel for nonlinear version of FKT, we have applied a compositional kernel combination approach to capture the underlying local distributions of hyperspectral remote sensing data. Optimal parameter selection for each kernel function is achieved applying an evolutionary technique called differential evolution algorithm. The proposed new nonlinear target detection algorithm is tested for hyperspectral images. The experimental results verify that the proposed target detection algorithm has effective and promising performance compared to the conventional version for supervised target detection applications.