Ultrasound imaging is widely used in medical diagnosis. It has the advantages of being performed in real time, cost-efficient, noninvasive, and nonionizing. The traditional delay-and-sum (DAS) beamformer has low resolution and contrast. Several adaptive beamformers (ABFs) have been proposed to improve them. Although they improve image quality, they incur high computation cost because of the dependence on data at the expense of real-time performance. Deep-learning methods have been successful in many areas. They train an ultrasound imaging model that can be used to quickly handle ultrasound signals and construct images. Real-valued radio-frequency signals are typically used to train a model, whereas complex-valued ultrasound signals with complex weights enable the fine-tuning of time delay for enhancing image quality. This work, for the first time, proposes a fully complex-valued gated recurrent neural network to train an ultrasound imaging model for improving ultrasound image quality. The model considers the time attributes of ultrasound signals and uses complete complex-number calculation. The model parameter and architecture are analyzed to select the best setup. The effectiveness of complex batch normalization is evaluated in training the model. The effect of analytic signals and complex weights is analyzed, and the results verify that analytic signals with complex weights enhance the model performance to reconstruct high-quality ultrasound images. The proposed model is finally compared with seven state-of-the-art methods. Experimental results reveal its great performance.