Single-inductor multiple-output (SIMO) LED drivers have the advantages of being compact, efficient and low cost. However, the voltage-to-current transfer function of each output of the SIMO converter is not independent, with significant cross regulation issues that necessitate the use of complex closed-loop control for achieving independent dimming function. This paper proposes a current-source-mode (CSM) SIMO dc-dc converter from duality principle, which is shown to be more suited for LED driving due to widened control range of the duty cycle and inherently inductor-less LED driving topology. The outputs of the CSM SIMO dc-dc converter are inherently independent, resulting in very simple control requirement involving only one closed-loop controller for providing the constant current feeder, and several simple open-loop controllers for independent dimmable driving of LEDs. Simultaneous voltage step-up and step-down of multiple outputs is an added feature that simplifies the input power source requirement especially for portable applications. The whole system is simple, reliable and low cost. Taking the CSM single-inductor dual-output (SIDO) dc-dc converter as an example, we illustrate the circuit operation and establish a small-signal model for facilitating the design of the feedback control. A direct duty-cycle dimming method is described. Experimental tests are presented for verification.