This paper presents a predictive model for estimating regularization parameters of diffeomorphic image registration. We introduce a novel framework that automatically determines the parameters controlling the smoothness of diffeomorphic transformations. Our method significantly reduces the effort of parameter tuning, which is time and labor-consuming. To achieve the goal, we develop a predictive model based on deep convolutional neural networks (CNN) that learns the mapping between pairwise images and the regularization parameter of image registration. In contrast to previous methods that estimate such parameters in a high-dimensional image space, our model is built in an efficient bandlimited space with much lower dimensions. We demonstrate the effectiveness of our model on both 2D synthetic data and 3D real brain images. Experimental results show that our model not only predicts appropriate regularization parameters for image registration, but also improving the network training in terms of time and memory efficiency.