Automatic target detection is an important application in the hyperspectral image processing field. Several target detection algorithms have been developed for hyperspectral images. However, most target detection algorithms were designed to detect one kind of target, and the number of multiple-target detection algorithms is very limited. Besides, the existing multiple-target detection algorithms use second-order statistics, which could characterize Gaussian data well. But for real hyperspectral images, spectra of targets usually do not follow Gaussian distribution. Under such circumstances, we propose a novel multiple-target detection algorithm, named regularized non-Gaussianity based multiple-target detector (RNGMD), which uses the non-Gaussianity statistics to characterize the statistical characteristics of targets' spectra. The RNGMD turns the multiple-target detection into a constrained optimization problem, and utilizes the gradient descent method to solve the optimization problem. Also, we prove the stability of the algorithm. The experimental results demonstrate that the proposed algorithm is more effective than second-order statistics based algorithms.