Spin-wave interference is demonstrated in the micromagnetic modeling of a specially designed geometry made of variously shaped magnetic thin-film waveguides. When spin waves are diffracted through two separate openings, corresponding to the two pinholes in the second screen of Young's apparatus, they interfere constructively or destructively in a magnetic medium, thereby showing distinct interference patterns. Furthermore, the radiation, propagation, transmission, and dispersion behaviors of spin waves as well as the filtering of their lower frequencies are investigated in the present modeling study. These results directly confirm not only the wave characteristics of spin waves traveling at ultrafast speeds in variously shaped magnetic waveguides but also their interference effect, that is similar to that observed in well-known Young's double slit experiment with light.