Improved measures are taken on existing damping current observer. Runge-Kutta (R-K4) is adopted to the improved observer which has higher accuracy, comparing with the old observer which adopted one-order forward difference. Initial value and absolute stability region of the observer are discussed and the condition when the initial value and the time observer taken into operation have no influence on result is given. By observing damper current of synchronous generator in IEEE first bench case for SSR, validity of improved damper current observer is testified. Damper current components are analyzed and using damper current to monitor SSO is proposed.