Owing to the nonlinearity in visual-inertial state estimation, sufficiently accurate initial states, especially the spatial and temporal parameters between IMU (Inertial Measurement Unit) and camera, should be provided to avoid divergence. Moreover, these parameters are required to be calibrated online since they are likely to vary once the mechanical configuration slightly changes. Recently, direct approaches have gained popularity for their better performance than feature-based approaches in little-texture or low-illumination environments, taking advantage of tracking pixels directly. Based on these considerations, we perform a direct version of monocular VIO (Visual-inertial Odometry), and propose a novel approach to initialize the spatial-temporal parameters and estimate them with all other variables of interest (IMU pose, point inverse depth, etc.). We highlight that our approach is able to perform robust and accurate initialization and online calibration for the spatial and temporal parameters without utilizing any prior information, and also achieves high-precision estimates even when large temporal offset occurs. The performance of the proposed approach was verified through the public UAV (Unmanned Aerial Vehicle) dataset.