The recent research shows that data-driven inertia navigation technology can significantly alleviate the drift error of Micro-Electro-Mechanical System Inertial Measurement Unit (MEMS-IMU) in pedestrian localization. However, most existing methods must rely on attitude information provided by external procedure (such as smartphone API), which violates the original intention of full autonomy of inertial navigation, and attitude information is also inaccurate. To address the problem, we propose a pedestrian indoor neural inertial navigation system that does not rely on external information and is only based on low-cost MEMS-IMU. First, a deep learning based neural inertial network was designed to estimate attitude. Then, in order to obtain position estimation with both global and local accuracy, an Invariant Extended Kalman Filter (IEKF) framework was proposed, where 3D displacement and its uncertainty regressed by a deep residual network are utilized to update IEKF. Extensive experimental results on a public dataset and a self-collected dataset show that the proposed method provides accurate attitude estimation and outperforms state-of-the-art methods in position estimation, demonstrating the superiority of our method in reliability and accuracy.