A quantitative structure-activity relationship (QSAR) investigation was done for the acute oral mammalian toxicity (LD50) of a set of 54 organophosphorus pesticide compounds. The compounds were represented with calculated molecular structure descriptors, which encoded their topological, electronic, and geometrical features. Feature selection was done with a genetic algorithm to find subsets of descriptors that would support a high quality computational neural network (CNN) model to link the structural descriptors to the - log(mmol/kg) values for the compounds. The best seven-descriptor non-linear CNN model found had an rms error of 0.22 log units for the training set compounds and 0.25 log units for the prediction set compounds.