We design an artificial limit-cycle oscillator that can achieve global in-phase synchronization under linear mutual coupling. Using a method for designing the vector field of a dynamical system with a prescribed limit cycle that we proposed recently based on phase reduction theory, we design a limit-cycle oscillator with a complex trajectory but without high-harmonic components in the phase response properties, which yields a phase coupling function with a globally stable in-phase fixed point. We provide an example of the designed oscillator and demonstrate its global in-phase synchronization dynamics by numerical simulations.