Multi-party learning is an indispensable technique for improving the learning performance via integrating data from multiple parties. Unfortunately, directly integrating multi-party data would not meet the privacy preserving requirements. Therefore, Privacy-Preserving Machine Learning (PPML) becomes a key research task in multi-party learning. In this paper, we present a new PPML method based on secure multi-party interactive protocol, namely Multi-party Secure Broad Learning System (MSBLS), and derive security analysis of the method. The existing PPML methods generally cannot simultaneously meet multiple requirements such as security, accuracy, efficiency and application scope, but MSBLS achieves satisfactory results in these aspects. It uses interactive protocol and random mapping to generate the mapped features of data, and then uses efficient broad learning to train neural network classifier. This is the first privacy computing method that combines secure multi-party computing and neural network. Theoretically, this method can ensure that the accuracy of the model will not be reduced due to encryption, and the calculation speed is very fast. We verify this conclusion on three classical datasets.