Transient analysis of Switching Power Converter (SPC) circuits is a computationally expensive task. This high expense arises from the fact that these circuits are driven by a clock with a period that is very small compared to the time interval the designer is typically interested in. Envelope-Following (EF) technique has been recently proposed in the literature for efficient time-domain simulation of SPC circuits. In this paper, a parallel high-order EF method, which is based on Obreshkov-Formula, is presented for analysis of SPC circuits. A numerical example is presented to demonstrate the efficiency and scalability of the proposed method on parallel platforms.