Logistic regression is a widely used machine learning model for real-world classification tasks. With the emerging ``isolated data islands" problem, it has become a key issue to collaboratively construct a logistic regression model based on non-penetrating data distributed in different data owners (multi-owner distribution). Vertical federated learning can realize the collaborative model training under multi-owner cross-feature data distribution while protecting the data plain-text from exposure. However, existing vertical federated logistic regression methods are mainly based on homomorphic encryption schemes, which would incur tremendous computation and communication costs. Therefore, this paper studies the secure and efficient vertical federated learning algorithm for the logistic regression model, aiming to achieve a better trade-off between data privacy protection and model learning efficiency. In particular, this paper proposes an efficient vertical federated learning algorithm VFLR-SS based on secret sharing. By randomly decomposing the intermediate data in the modeling process into multiple secret shares,  VFLR-SS can achieve privacy protection while avoiding the computational and communication overhead caused by homomorphic encryption algorithms. In this paper, the security analysis of VFLR-SS is provided, and the effectiveness and efficiency of the algori-thm are verified based on real data. The experimental results demonstrate that VFLR-SS can achieve comparable effectiveness and efficiency to centralized logistic regression algorithms, and significantly reduce the computation and communication costs in traditional homomorphic encryption schemes.