Target detection in hyperspectral images (HSIs) is an active area of research; it seeks to detect objects that are small in both number and size within a scene. The proposed work presents a new methodology for target detection in HSIs by combining kurtosis, level sets, and a size-based thresholding strategy. Kurtosis is used as a preprocessing step to initially enhance the targets in an image. Then, level sets identify and mark associations of pixels with similar spectral information as candidate targets. Finally, the size-based thresholding strategy detects true targets and discards false alarms that do not fit with target dimensions set as input parameter. In addition, we propose a novel version of level sets, which is suitable for target detection tasks in HSIs. Results show that the proposed algorithm could successfully detect targets in HSIs, and it gave better performance in terms of the receiver operating characteristic curve than other techniques widely used in target detection such as orthogonal subspace projection, constrained signal detector, constrained energy minimization, adaptive cosine/coherent estimator algorithm, and generalized-likelihood ratio test.