Quantum memory is a key enabling component for quantum communication and large-scale quantum networks, as it allows for the storage and on-demand retrieval of quantum states while preserving their coherence and fidelity. In particular, time-multimode quantum storage, which enables the simultaneous storage of multiple temporal modes, plays a crucial role in improving communication rates and expanding storage capacity. In this work, we propose a high-efficiency time-multimode quantum storage scheme based on electromagnetically induced transparency (EIT) in cold atomic ensembles. By dynamically tailoring the Rabi frequency of the control field and optimizing the switching-off process of the control field, the storage and retrieval processes of multi-pulse photons are coherently controlled. A theoretical model is developed to systematically analyze the storage performance under large optical depth conditions. The results show that the proposed scheme can simultaneously achieve high storage efficiency and large multimode capacity. Specifically, the storage efficiency exceeds 70% for multiple temporal modes and can reach up to ~90% in the few-mode regime. Furthermore, we quantitatively reveal that the number of accessible temporal modes is fundamentally limited by the optical depth, and demonstrate that both storage capacity and efficiency can be significantly improved through optimization of the medium parameters. These results provide an effective approach to overcoming the trade-off between storage capacity and efficiency in quantum memory, and offer a promising route toward high-throughput quantum information processing and long-distance quantum communication.