In this presentation we propose a new iterative method for the solution of linear systems with a p-cyclic coefficient matrix. These p-cyclic matrices arise in the periodic steady state simulation of circuits, assumed that the DAE is discretized in the time domain. The matrix has a p-cyclic structure since the end of the periodic time interval is coupled with the begin of the interval. The new method has similarities with existing GMRES approaches for p-cyclic matrices, but in contrast to these methods the method is well parallelizable, even if the p-cyclic matrix has a small block size. Moreover it has good stability properties. However, the sequential costs of the new method may be higher. The effectiveness of the method will be showed by numerical experiments.