Fly-buck converter is a multi-output converter with the structure of a synchronous buck converter structure on the primary side and a flyback converter structure on the secondary side, and can be utilized in various applications due to its many advantages. In terms of control, the primary side of the fly-buck converter has the same structure as a synchronous buck converter, allowing the constant-on-time (COT) control to be applied to the fly-buck converter. However, due to the inherent energy transfer principle, the primary-side output voltage regulation of COT controlled fly-buck converters may be poor, which can deteriorate the overall converter performance. Therefore, the primary output capacitor must be carefully designed to improve the voltage regulation characteristics. In this paper, a theoretical analysis of the output voltage regulation in COT controlled fly-buck converter is conducted, and based on this, a design guideline for the primary output capacitor considering the output voltage regulation is presented. The validity of the analysis and design guidelines was verified using a 5 W prototype of the COT controlled fly-buck converter for telecommunication auxiliary power supply.