Vertically partitioned data is distributed data in which information about a patient is distributed across multiple sites. In this study, we propose a novel algorithm (referred to as VdistCox) for the Cox proportional hazards model (Cox model), which is a widely-used survival model, in a vertically distributed setting without data sharing. VdistCox with a single hidden layer feedforward neural network through extreme learning machine can build an efficient vertically distributed Cox model. VdistCox can tune hyperparameters, including the number of hidden nodes, activation function, and regularization parameter, with one communication between the master site, which is the site set to act as the server in this study, and other sites. In addition, we explored the randomness of hidden layer input weights and biases by generating multiple random weights and biases. The experimental results indicate that VdistCox is an efficient distributed Cox model that reflects the characteristics of true centralized vertically partitioned data in the model and enables hyperparameter tuning without sharing information about a patient and additional communication between sites.