The integration of deep learning methods with physical equation constraints has become a dominant development trend of seismic Full-Waveform Inversion (FWI). At present, physically constrained deep learning-based FWI is mostly implemented based on automatic differentiation frameworks. However, when applied to large-scale numerical simulations, such frameworks suffer from excessive gradient memory consumption, poor adaptability of gradient preprocessing, and difficulties in model segmentation computation, which limit their practical application for subsurface velocity modeling. To address these issues, this study abandons the gradient calculation scheme of automatic differentiation and adopts the adjoint gradient computation of conventional FWI as the core algorithm. Combined with deep learning reparameterization technology and network optimization training strategies, a more practical deep learning parameterized FWI method is proposed. Relying on high-performance computing resources, the adjoint-state gradient of the convolution-based objective function is efficiently solved. A Long Short-Term Memory Neural Network (LSTM-NN) is employed to characterize subsurface model parameters. Leveraging its superior capability in capturing long-range dependencies, the network establishes a more stable parameter mapping relationship and effectively improves the performance of network reparameterization. Furthermore, targeting the strong nonlinearity inherent in FWI, a multi-scale inversion strategy is introduced. Independent LSTM-NN parameterized training is performed at different inversion scales, enabling the network to characterize subsurface medium information layer by layer and effectively enhance the global convergence performance of the algorithm. Numerical test results verify that compared with the conventional convolutional neural network-based parameterized inversion method, the proposed LSTM-NN multi-scale inversion method can clearly delineate subsurface structural interfaces, compensate for the deficiencies of geometry illumination, and significantly improve the identification accuracy of fault details. It ultimately delivers inversion results with higher accuracy, providing a feasible technical solution for the practical application of high-precision seismic velocity modeling.