Neural networks have shown great potential in many applications like speech recognition, drug discovery, image classification, and object detection. Neural network models are inspired by biological neural networks, but they are optimized to perform machine learning tasks on digital computers. The proposed work explores the possibilities of using living neural networks in vitro as basic computational elements for machine learning applications. A new supervised STDP-based learning algorithm is proposed in this work, which considers neuron engineering constrains. A 74.7% accuracy is achieved on the MNIST benchmark for handwritten digit recognition.