Sine inverter is a time varying nonlinear system, for which two scales, namely the fast and slow-scale, can be used to analyses its stability. Based on this, fast- and slow-scale discrete model of H-bridge sine inverter under proportional control are derived respectively. For the fast-scale stability, folded diagram and spectrum analysis are introduced. For the slow-scale stability, slow-scale fixed points and a theorem of slow-scale instability of a discrete-time periodically varying system are proposed. It is shown that slow-scale instability is an effective criterion for chaos motions of discrete-time periodically varying system. Research shows that proposed methods can be used to analyse the fast- and slow-scale instability and chaotic behavior of H-bridge sine inverter.