The hazardous psychoactive designer drugs are compounds in which part of the molecular structure of a stimulant or narcotic has been modified. A quantitative structure-retention relationship (QSRR) study based on a Levenberg-Marquardt artificial neural network (L-M ANN) was carried out for the prediction of the capacity factor (k′) of hazardous psychoactive designer drugs that contain Tryptamine, Phenylethylamine and Piperazine. The genetic algorithm-partial least squares (GA-PLS) method was used as a variable selection tool. A PLS method was used to select the best descriptors and the selected descriptors were used as input neurons in neural network model. For choosing the best predictive model from among comparable models, square correlation coefficient (R2) for the whole set is suggested to be a good criterion. Finally, to improve the results, structure-retention relationships were followed by nonlinear approach using artificial neural networks and consequently better results were obtained. Also this demonstrates the advantages of L-M ANN. This is the first research on the QSRR of the designer drugs using the GA-PLS and L-M ANN.