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In this article, we focus on the existence and stability of a subsonic global solution in an infinitely long curved nozzle for the three-dimensional steady potential flow equation. By introducing some suitably weighted Holder spaces and establishing a series of a priori estimates on the solution to second order linear elliptic equation in an unbounded strip domain with two Neumann boundary conditions and one periodic boundary condition with respect to some variable, we show that the global subsonic solution of potential flow equation in a 3-D nozzle exists uniquely when the state of subsonic flow at negative infinity is given. Meanwhile, the asymptotic state of the subsonic solution at positive infinity as well as the asymptotic behavior at minus infinity are also studied.