Hybrid conduction mode (HCM) is gradually applied in single-inductor dual-output (SIDO) dc-dc converter as its advantages of reducing switching loss and minimizing cross-regulation. However, it shows that the circuit parameters will affect the stability and restrict its operation range, which causes the converter to operate in non-HCM and these advantages are lost. In this paper, to figure out this phenomenon, eight different operation modes of the HCM SIDO buck converter are analyzed. On this basis, a three-dimensional discrete-time model, which is suitable for variable-frequency control, is established. And then, the effect of output capacitors and its equivalent series resistances (ESRs), load resistors, input voltage and output voltages, constant turn-off time on the stability is discussed. The study results show that the stability and operation mode is sensitive to the difference circuit parameters and control parameters. In addition, the dynamic ramp-compensation based on inductor current is proposed and analyzed for stabilization control, which can broaden the stable operation range of this converter. Finally, experimental results validate the accuracy of proposed theoretical analysis.