One of the food preservation technologies is the drying process, which requires heat and is significantly energy-intensive, resulting in high costs. This caused the search for new design solutions for dryers, which requires continuous experimental research and the creation of new decision-supporting models for the optimization of drying processes. In this work, four models of the kinetics of convective onion drying were developed using Artificial Neural Networks (ANNs), taking into account pre-treatment before drying and the different temperatures of the drying agent. The moisture content in the dried material at a specific moment in time was taken as the dependent variable (ANN output). The following were accepted as independent variables (ANN inputs): drying temperature, initial sample thickness, initial moisture content, initial mass of the sample, time of drying, and material pre-treatment (no pre-treatment—blanching–osmotic dehydration). Four semantic models were formulated, the general Ann1 model taking into account all input variables and three detailed Ann2 models for individual types of pre-treatment. For the best Ann1, the MAPE values were 5.88–7.02% (for different data: Training, Test, Validation). For the detailed Ann2 models, the error values were more than twice lower. The MAPE values ranged from 1.14% to 3.12%.