In this paper, two problems of quasi-resonant interactions among barotropic Rossby waves over a two-wave topography are investigated. The first one is the study of three-wave quasi-resonance (TWQR) among Rossby waves for zonal wavenumbers 1–3 in which zonal waves 1 and 3 travel westward and eastward respectively, and zonal wave 2 is a quasi-stationary wave forced by two-wave topography (TWT). It is found that, in the absence of TWT, three-wave quasi-resonance will induce a nearly 7–10 day oscillation. However, under the forcing of TWT, a remarkable 30–60 day low-frequency oscillation (LFO) can be excited through TWQR, and found to depend considerably upon the initial amplitudes of these waves and the latitude. The second is the study of four-wave quasi-resonance (FWQR) among Rossby waves for the zonal wavenumbers 1–4 and same meridional wavelength over a two-wave topography that is independent of the meridional coordinate. It is shown that for the small meridional wavelength the four-wave quasi-resonance without forcing can lead to a 30–60 day LFO, which relies equally upon the initial amplitudes and latitude. However, once the forcing of TWT is considered, such a LFO is greatly affected by the zonal basic westerly wind and remains within the 30–60 day period band under favorable conditions. Moreover, in the limit of large meridional wavelength where a quasi-biweek oscillation only appears for the case without forcing, a 30–60 day LFO can occur for zonal waves 1–3 in the presence of TWT and under a moderate zonal basic westerly wind. This indicates that a moderate setting of zonal basic westerly wind favors a 30–60 day LFO.