This paper presents an artificial neural network (ANN)-based nonlinear model predictive visual servoing method for mobile robots. The ANN model is developed for state predictions to mitigate the unknown dynamics and parameter uncertainty issues of the physics-based (PB) model. To enhance both the model generalization and accuracy for control, a two-stage ANN training process is proposed. In a pretraining stage, highly diversified data accommodating broad operating ranges is generated by a PB kinematics model and used to train an ANN model first. In the second stage, the test data collected from the actual system, which is limited in both the diversity and the volume, are employed to further finetune the ANN weights. Path-following experiments are conducted to compare the effects of various ANN models on nonlinear model predictive control and visual servoing performance. The results confirm that the pretraining stage is necessary for improving model generalization. Without pretraining (i.e., model trained only with the test data), the robot fails to follow the entire track. Weight finetuning with the captured data further improves the tracking accuracy by 0.07–0.15 cm on average.