The industry uses Fused Deposition Modeling (FDM) in the manufacture of the final products through the additive manufacturing method (AM). Due to this approach, one can construct a prototype and other components with complicated geometry, which not only translates into the saving of expensive dollars but also makes the project more flexible. Printing and material type, as well as other processing settings, affect the nature of parts, in terms of mechanics as well as other aspects. This paper attempts to develop a model to predict the mechanical capabilities and surface quality of FDM-printed ABS objects based on Artificial Neural Networks. Taguchi design of experiments is applied with an L27 orthogonal array coupled with a two-layer Neural Network (NN) with 15 neurons. The impact of the characteristics of the layer height, the orientation angle, and the nozzle temperature on the strength and finish of parts was investigated by means of the analysis of variance (ANOVA). Layer thickness seemed to be the major variable in the analysis because it was identified to create over 43.67% variation in ultimate tensile strength and 46.38% variation in surface roughness. The predicted results by the model were just a little different compared with the actual results. The highest percent error in the tensile strength and the surface roughness are 2.346 and 1.876, respectively, which arises when comparing the experimental and predicted values as calculated using the ANN model. With such a model, different parameters selected are able to achieve the requirements of a particular application.