We study mode switching (MS) between information decoding and energy harvesting (EH) for simultaneous wireless information and power transfer (SWIPT) over the fading channel. Unlike the existing result obtained with a simplistic assumption of linear EH, we consider a realistic scenario of the nonlinear EH. In this setting, to design the optimal MS, we address the problem of maximizing the average achievable rate under an average harvested energy constraint, which is generally nonconvex and combinatorial. Using the time-sharing condition, the optimal MS solution for the nonlinear EH is presented efficiently. From the obtained result and further analysis, we draw interesting and important insights into the optimized SWIPT system with nonlinear EH.