In the aim of improving the positioning accuracy of the monocular visual-inertial simultaneous localization and mapping (VI-SLAM) system, an improved initialization method with faster convergence is proposed. This approach is classified into 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 the IMU and camera was aligned by IMU pre-integration 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.