This paper demonstrates a single-inductor dual-output (SIDO) buck converter, which is developed for implantable medical devices. The dual-mode operation, which combines pulse-skip modulation (PSM) and pulse-width modulation (PWM), is employed to regulate outputs under light load and heavy load conditions, respectively. The converter provides two output voltages: VOUT1 (2.5-3V) for charge pumps and VOUT2 (2V) for digital circuits. With the start-up circuits, the SIDO buck converter can act as self-start-up DC-DC buck converter. To avoid voltage stress issue under 3.2-4.2V battery operation in 180nm standard (CMOS) process, the stacked power stage is used. The proposed level shifter includes an additional level restorer to avoid a misjudgment issue during start-up period. The simulation results demonstrate that the converter achieves peak efficiency of 94.5% with PSM control, and it achieves peak efficiency of 89.1% with PWM control.