The target-constrained interference-minimized filter (TCIMF) method has been successfully applied to various hyperspectral target detection applications. This paper presents a nonlinear version of TCIMF, called kernel-based TCIMF (KTCIMF), employing the kernel method to resolve the issue of nonlinear endmember mixing in hyperspectral images (HSI). Input data are implicitly mapped into a high-dimensional feature space, where it is assumed that target signals are more separable from background signals. Conventional TCIMF performs well in suppressing undesired signatures whose spectra are similar to that of the targets, thereby enhancing performance, and with less false alarms. KTCIMF not only takes into consideration the nonlinear endmember mixture but also fully exploits the other spectrally similar interference signatures. In this way, it is effective in suppressing both the background and those undesired signatures that may cause false alarms in traditional methods. Experimental results with both simulated and real hyperspectral image data confirm KTCIMF's performance with intimately mixed data. Compared with conventional kernel detectors, KTCIMF shows improved ROC curves and better separability between targets and backgrounds.