Recently, the low frequency oscillation (LFO) frequently happens in the vehicle grid system of high speed railways when electric multiple units (EMUs) are put into operation. As a possible solution, a single phase cascaded H-bridge static synchronous compensator (CHB-STATCOM) directly connected to the traction network is applied to dynamically compensate the reactive power of vehicle grid system. This project proposes on the impedance modeling and stability analysis in the vehicle grid system with CHB-STATCOM. Firstly, the vehicle grid system is simplified to a single phase rectifier with large grid inductance. The accurate dq-frame impedance of the rectifier system with CHB-STATCOM is derived in detail. Secondly, through the generalized Nyquist stability criterion (GNSC), the influence of CHB-STATCOM and its different control parameters on the stability of rectifier system is revealed. Thirdly, the excellent performance of CHB-STATCOM in suppressing the LFO and the accuracy of theoretical analysis are verified via time domain simulations. Finally, to further verify the effectiveness of CHB-STATCOM in real applications, a DSPICK based controller hardware in the loop (HIL) simulation platform is established which includes the physical control circuits of eight EMUs. The experimental results show that the CHB-STATCOM has a good dynamic compensation effect and can efficiently suppress the LFO.