Low-cost　microelectro　mechanical　systems　(MEMS)-based　inertial　measurement　unit　(IMU)　measurements　are　usually　affected　by　inaccurate　scale　factors,　axis　misalignments,　and　g-sensitivity　errors.　These　errors　may　significantly　influence　the　performance　of　visual-inertial　methods.　In　this　paper,　we　propose　an　online　IMU　self-calibration　method　for　visual-inertial　systems　equipped　with　a　low-cost　inertial　sensor.　The　goal　of　our　method　is　to　concurrently　perform　3D　pose　estimation　and　online　IMU　calibration　based　on　optimization　methods　in　unknown　environments　without　any　external　equipment.　To　achieve　this　goal,　we　firstly　develop　a　novel　preintegration　method　that　can　handle　the　IMU　intrinsic　parameters　error　propagation.　Then,　we　frame　IMU　calibration　problem　into　general　factors　so　that　we　can　easily　integrate　the　factors　into　the　current　graph-based　visual-inertial　frameworks　and　jointly　optimize　the　IMU　intrinsic　parameters　as　well　as　the　system　states　in　a　big　bundle.　We　evaluate　the　proposed　method　with　a　publicly　available　dataset.　Experimental　results　verify　that　the　proposed　approach　is　able　to　accurately　calibrate　all　the　considered　parameters　in　real　time,　leading　to　significant　improvement　of　estimation　precision　of　visual-inertial　system　(VINS)　compared　with　the　estimation　results　with　offline　precalibrated　IMU　measurements.