In this paper, we use synthetic data and propose a new method to reconstruct high-resolution face images from facial templates in a template inversion attack against face recognition systems. We use a pre-trained face generator network to generate synthetic face images, and then learn a mapping from the facial templates to the intermediate latent space of the face generator network. We train our mapping network with a multi-term loss function. During the inference stage, we use our mapping network to map facial templates to the intermediate latent code and then generate high-quality face images using the face generator network. We propose our method for whitebox and blackbox template inversion attacks against face recognition systems. We use our model (trained on synthetic data) to evaluate the vulnerability of state-of-the-art face recognition systems on real face datasets, including Labeled Faces in the Wild (LFW) and MOBIO datasets. Experimental results show the vulnerability of the state-of-the-art face recognition system to our template inversion attack. Our experiments also show that our template inversion method outperforms previous methods in the literature. The source code of our experiments is publicly available to facilitate reproducibility of our work.