With the popularity of artificial intelligence and cloud computing, many neural network models can be placed on the cloud server as an open service, such as Google Goggles and the online face recognition system of Baidu. The data owner sends his data to the cloud server to get the prediction result of data. Obviously, the cloud service provider can access model parameters and private data if there is no additional protection mechanism. On the one hand, if the adversary can access private data, they can freely use the artificial intelligence model and Big Data technologies to analyze the data owner. On the other hand, when the adversary can access model parameters, the interest of model owner would be harmed. Thus, preserving model parameters (model privacy) and private data (data privacy) becomes the key for applying neural network models as open cloud services. In this article, to protect the model privacy and data privacy in neural network prediction even when a cloud service provider colludes with the data owner or the model owner, we first propose a new system model with two no-colluding cloud servers and a corresponding security model. Then, we propose a new non-interactive outsourcing scheme, which can protect model privacy together with data privacy. Our scheme is able to resist collusive attacks of one server and the data owner as well as collusive attacks of one server and the model owner. At last, the security analyses indicate that our scheme just needs no collusion between cloud servers. The performance analyses indicate that our scheme is very lightweight for the data owner, and it is about tens of milliseconds for a neural network model with 1000 parameters.