Self-powered synchronized switching harvesting on an inductor (SSHI) circuits have been proved to greatly increase the performance of a PVEH device and peak detector-based self-powered switches are widely used. In practice, however, the switch is impossible to turn on simultaneously at peak displacements due to nonlinear components, so that switching delay(SD) always exists. Furthermore, the SD will degrade the performance of PVEH devices, so it must be reduced. Therefore, for this kind of SSHI circuits, the purpose of this paper is to explore basic causes of generating SD and investigate the corresponding solution. Firstly, theoretical model of SD in self-powered parallel (SP-PSSHI) is derived and the SD is first proved to be positive. Then effects of key component parameters on the SD are studied. Based on above results, an improved SP-PSSHI (ISP-PSSHI) circuit is proposed by adding a voltage divider and its SD is proved to be less than that of the SP-PSSHI circuit. Circuit simulations validate theoretical results and also expose that there are optimal resistor and capacitor of the envelope detector for achieving the maximum harvested power. In the end, experimental results show that the ISP-PSSHI circuit can improve the averaged harvested power about 11 percent more than that of the SP-PSSHI circuit under choosing optimal components.