<p>We consider a discrete-time competition model between native and alien predator populations for a common prey. The model is described by a system of three recurrence relations governing their population dynamics, with a generic density-dependent effect for prey and a generic predation factor. In our model, the native and alien predators prey on different stages of the common prey: juvenile-specific and adult-specific predators. In this paper, we focus on the invadability of native prey-predator system to an alien predator and investigate which stage-specific alien predator could be more successful in invading the native system with a different stage-specific native predator. Our mathematical results demonstrate that the prey-predator system with an adult-specific native predator is more vulnerable to the juvenile-specific alien predator invasion compared to the native system with a juvenile-specific native predator. To illustrate the general result more clearly, we present some detailed results on a specific model with a Beverton-Holt type of density-dependent effect and a Nicholson-Bailey type of predation factor, which effectively demonstrates such the dependence of vulnerability to an alien predator invasion on the stage-specific predation.</p>