Using a global spectral model of the quasi-geostrophic barotropic vorticity equation, numerical study is made of the quasi-resonance interaction of three planetary waves.With two quasi-resonance wavevectors selected as 1)K₁+K₂+K₃=0,ω₁+ω₂+ω₃=Δω; 2)k₁+k₂+k₃=0, l₁+l₂+l₃=Δl,ω₁+ω₂+ω₃=0,model integrations are run for 90 days,separately,leading to the results of interest as follows:1)stronger wave-wave interplay is found among the three waves of zonal wavenumber k=1,2,3; 2)due to the interactions,the study waves exhibit about 20-45-day low-frequency oscillations and it is of note that all of the waves display quasi-biweekly oscillations; 3)the mentioned low-frequency periods relate to the initial amplitude of the waves under investigation.