Beamforming is a key technology in communication systems of the fifth generation and beyond. However, traditional optimization-based algorithms are often computationally prohibited from performing in a real-time manner. On the other hand, the performance of existing deep learning (DL)-based algorithms can be further improved. As an alternative, we propose an unsupervised ResNet-inspired beamforming (RI-BF) algorithm in this paper that inherits the advantages of both pure optimization-based and DL-based beamforming for efficiency. In particular, a deep unfolding technique is introduced to reference the optimization process of the gradient ascent beamforming algorithm for the design of our neural network (NN) architecture. Moreover, the proposed RI-BF has three features. First, unlike the existing DL-based beamforming method, which employs a regularization term for the loss function or an output scaling mechanism to satisfy system power constraints, a novel NN architecture is introduced in RI-BF to generate initial beamforming with a promising performance. Second, inspired by the success of residual neural network (ResNet)-based DL models, a deep unfolding module is constructed to mimic the residual block of the ResNet-based model, further improving the performance of RI-BF based on the initial beamforming. Third, the entire RI-BF is trained in an unsupervised manner; as a result, labelling efforts are unnecessary. The simulation results demonstrate that the performance and computational complexity of our RI-BF improves significantly compared to the existing DL-based and optimization-based algorithms.