Inconel 718 is a nickel-based superalloy and an excellent candidate for the aerospace, oil, and gas industries due to its high strength and corrosion resistance properties. The machining of IN718 is very challenging; therefore, the application of additive manufacturing (AM) technology is an effective approach to overcoming these difficulties and for the fabrication of complex geometries that cannot be manufactured by the traditional techniques. Selective laser melting (SLM), which is a laser powder bed fusion method, can be applied for the fabrication of IN718 samples with high accuracy. However, the process parameters have a high impact on the properties of the manufactured samples. In this study, a prediction model is developed for obtaining the optimal process parameters, including laser power, hatch spacing, and scanning speed, in the SLM process of the IN718 alloy. For this purpose, artificial neural network (ANN) modeling with various algorithms is employed to estimate the process outputs, namely, sample height and surface hardness. The modeling results fit perfectly with the experimental output, and this consequently proves the benefit of ANN modeling for predicting the optimal process parameters.