When a liquid approaches its glass-transition temperatures T-g, the structural relaxation time tau dramatically increases. This basic feature is ubiquitous, but this increase of tau can be classified between strong and fragile extremes using T-g as a scaling parameter. Liquids, whose tau obeys the Arrhenius law, are called "strong," while "fragile" liquids have the super-Arrhenius behavior. Here we report the first continuous control of the fragility of liquid of the same material over a wide range of fragility, using a continuous liquid-liquid transition. Our study clearly demonstrates that the fragility is not a material-specific quantity, but is controlled by the order parameter governing the liquid-liquid transition, which may be the fraction of locally favored structures in the liquid.