Formation of compound droplets from a co-axial dual nozzle was simulated by a three-fluid front-tracking method. The device simulated in this study is the so-called flow-focusing device. Core and shell fluids, which are the constituents of a compound droplet, are injected from inner and outer nozzles, respectively. External fluid is also injected to drag the core and shell fluids and promote their breakup into droplets. The dripping-jetting transition was observed in a manner similar to the formation of simple droplets in two-fluid systems. The formation of compound droplets sometimes fails, and simple droplets with no core fluid are produced depending on the non-dimensional numbers. The transition between compound and simple droplets was examined by changing the Capillary number (Ca) of the core fluid and the ratio of the external fluid viscosity to the droplet fluid viscosity. When both the viscosity ratio and Ca are low, the droplets break off as simple droplets. When these numbers are moderate, compound droplets are formed. The Weber number of the core fluid also influences the formation of compound droplets.