In recent years, deep learning techniques have been widely applied in computational optical three-dimensional imaging. Fringe projection profilometry uses a trained deep neural network to recover high-precision phase information from a single fringe image. However, collecting the training dataset for a neural network expends a considerable amount of time and human resources. To mitigate this problem, we establish a digital twin-fringe projection system that enhances virtual fringe patterns using domain randomization techniques. A U-Net neural network is pretrained using a large number of simulated fringe-pattern images generated through virtual scanning. Next, transfer learning is introduced and the neural network parameters are fine-tuned using a small number of real fringe-pattern images. Targeting fringe analysis applications, this study proposes and analyzes three U-Net neural network fine-tuning schemes: “from left to right” “from top to bottom” “global fine-tuning”. The experimental results demonstrate that fine-tuning the bottleneck network module of the U-Net under the “from top to bottom” strategy optimizes the transfer learning results, largely improving the phase prediction accuracy of the neural network. The proposed method achieves high-precision phase reconstruction results after training the neural network on only 20% of the real data, thus avoiding the need for a large real dataset.