In the aim of improving the positioning accuracy of monocular visual inertial simultaneous localization and mapping (VI-SLAM) system, an improved initialization method with faster convergence is proposed. This approach is classified as three parts: Firstly, in the initial stage, the pure vision measurement model of ORB-SLAM is employed to make all the variables visible. Secondly, the frequency of IMU camera was aligned by IMU preintegration technology. Thirdly, an improved iterative method is put forward for estimating the initial parameters of IMU faster. The estimation of IMU initial parameters is divided into several simpler sub-problems, containing direction refinement gravity estimation, gyroscope deviation estimation, accelerometer bias and scale estimation. The experimental results on the self-built robot platform show that our method can up-regulate the initialization convergence speed, simultaneously improve the positioning accuracy of the entire VI-SLAM system.