Accurate classification of human blood cells plays a decisive role in the diagnosis and treatment of diseases. Artificial Neural Networks (ANN) have been consistently used as a trusted classification tool for this type of analysis. In this study, a new Artificial Neural Network approach is proposed for the multidimensional classification of two of the most common forms of leukemia: Acute Lymphoblastic Leukemia (ALL) and Acute Myeloid Leukemia (AML), also sometimes called Acute Myelogenous Leukemia. Beckman-Coulter Corporation supplied flow cytometry data of 120 patients that were used in the training and testing phases. The ANN algorithm was thus developed to exploit the different features of the different blood cells provided in an optimized fashion. The goal was to establish a programming tool, supported through this new ANN development, for the identification of normal and abnormal blood samples and provide information to medical doctors in the form of diagnostic references for the specific disease state that is considered for this study. The application of the ANN algorithm produced remarkable classification accuracy results that show a 95% classification accuracy for the normal blood samples and 90% classification accuracy for the abnormal samples even under the ubiquitous problem of overlap.