Distributed learning is a very effective divide-and-conquer strategy for dealing with big data. As distributed learning algorithms become more and more mature, network security issues including the risk of privacy disclosure of personal sensitive data, have attracted high attention and vigilance. Differential privacy is an important method that maximizes the accuracy of a data query while minimizing the chance of identifying its records when querying from this data. The known differential privacy distributed learning algorithms are based on variable perturbation and the variable perturbation method may be non-convergence and the experimental results usually have large deviations. Therefore, in this article we consider differential privacy distributed learning algorithm based on objective function perturbation. We first propose a new distributed logistic regression algorithm based on objective function perturbation (DLR-OFP). We prove that the proposed DLR-OFP satisfies differential privacy, and obtain a fast convergence rate by introducing a new acceleration factor for the gradient descent method. The numerical experiments based on benchmark data show that the proposed DLR-OFP algorithm has fast convergence rate and good privacy protection ability.