A method,stroboscopic harmonicbalance method which is used to solve strong nonlinear system, is proposed. The method is used to find the solution of strong nonlinear system. In investigation,the existence conditions of primary resonance solution and subharmonic resonance solutions are obtained. The results which are obtained by the stroboscopic harmonicbalance method are compared with those by computer numerical simulation. The results show that the stroboscopic harmonicbalance method is correct in qualitative analysis and it can meet the demands in engineering.