Ti–6Al–4V alloy has superior material properties such as high strength-to-weight ratio, good corrosion resistance, and excellent fracture toughness. Therefore, it is widely used in aerospace, medical, and automotive industries where machining is an essential process for these industries. However, machining of Ti–6Al–4V is a material with extremely low machinability characteristics; thus, conventional machining methods are not appropriate to machine such materials. Ultrasonic-assisted machining (UAM) is a novel hybrid machining method which has numerous advantages over conventional machining processes. In addition, minimum quantity lubrication (MQL) is an alternative type of metal cutting fluid application that is being used instead of conventional lubrication in machining. One of the parameters which could be used to measure the performance of the machining process is the amount of cutting force. Nevertheless, there is a number of limited studies to compare the changes in cutting forces by using UAM and MQL together which are time-consuming and not cost-effective. Artificial neural network (ANN) is an alternative method that may eliminate the limitations mentioned above by estimating the outputs with the limited number of data. In this study, a model was developed and coded in Python programming environment in order to predict cutting forces using ANN. The results showed that experimental cutting forces were estimated with a successful prediction rate of 0.99 with mean absolute percentage error and mean squared error of 1.85% and 13.1, respectively. Moreover, considering too limited experimental data, ANN provided acceptable results in a cost- and time-effective way.