An artificial neural network (ANN) approach was employed for the prediction and control of surface roughness (Ra and Rz) in a computer numerical control (CNC) machine. Experiments were performed on a CNC machine to obtain data used for the training and testing of an ANN. Experimental studies were conducted, and a model based on the experimental results was set up. Five machining parameters (cutter type, tool clearance strategy, spindle speed, feed rate, and depth of cut) were used. One hidden layer was used for all models, while there were five neurons in the hidden layer of the Ra and Rz models. The RMSE values were calculated as 1.05 and 3.70. The mean absolute percentage error (MAPE) values were calculated as 20.18 and 15.14, which can be considered as a good prediction. The results of the ANN approach were compared with the measured values. It was shown that the ANN prediction model obtained is a useful and effective tool for modeling the Ra and Rz of wood. The results of the present research can be applied in the wood machining industry to reduce energy, time, and cost.