A single-stage power converter, operating in either the burst or continuous mode for low-power energy sources, is presented in this brief. With the proposed converter, the energy from the ambient energy source is processed once (i.e., a single-step conversion process) before powering the load circuits, thereby allowing an increase in the overall efficiency once compared to two-step conversion processes. The proposed power converter is designed using off-the-shelf components consisting of a boost converter, a temporary storage element (i.e., supercapacitor) and an output switching circuit (OSC). The OSC is used to manage the duration period for the load that operates in either the burst or continuous mode. The proposed power converter can start the operation from an input voltage as low as 0.3 V and up-convert the output to about 3.7 V. This brief achieves a peak end-to-end efficiency of 70.06% through a single-step power conversion. The proposed power converter can support an output power range from 1 $\mu \text{W}$ to 202 mW. Once compared to prior work, the proposed power converter can achieve a wide dynamic load range, a higher end-to-end efficiency with a low input voltage as well as a single-step power conversion.