Current methods used to diagnose the thalassemia minor ™ patients require high-cost assays, while broader screening based on routine blood count has limited specificity and sensitivity. This study developed a new screening technique for TM patients’ diagnosis. The study enrolled 526 patients database that included 185 verified α and β TM cases, and control group consisted of iron-deficiency anemia (IDA), myelodysplastic syndrome (MDS), and healthy patients. More than 1,500 artificial neural networks (ANNs) models were created and the networks that gave high accuracy were selected for the study. TM patients were identified from the general database using the best-optimized ANNs. Comparison between three or six routine blood count parameters determined a slightly higher accuracy of the model with the three-parameter scheme, including mean corpuscular volume, red blood cell distribution width, and red blood cell. Based on these parameters, we were able to separate TM patients from the control group and MDS group, with specificity of 0.967 and sensitivity of 1. Including IDA patients into comparison gave lower but, still, very good values of specificity of 0.968 and sensitivity of 0.9. ANN-based TM diagnostics should be used for broad automatic screening of general population prior diagnosis with high-cost tests.