This study examines Quasi-Biennial Oscillation (QBO) teleconnections and their modulation by the El Niño-Southern Oscillation (ENSO), using a multi-model ensemble of the Atmospheric Processes And their Role in Climate (APARC) QBO initiative (QBOi) models. Some difficulties arise in examining observed QBO-ENSO teleconnections from distinguishing the QBO and ENSO influences outside of the QBO region, due to aliasing between the QBO and ENSO over the historical record. To separate the QBO and ENSO signals, simulations are conducted with annually-repeating prescribed sea-surface temperatures corresponding to idealized El Niño or La Nina conditions (QBOi EN and LN experiments, respectively). In the Arctic winter climate, higher frequencies of sudden stratospheric warmings (SSWs) are found in EN than LN. The frequency differences in SSW between QBO westerly (QBO-W) and QBO easterly (QBO-E) are indistinguishable, suggesting that the polar vortex responses to the QBO are much weaker than those to the ENSO in these models. The Asia-Pacific subtropical jet (APJ) shifts significantly equatorward during QBO-W compared to QBO-E in observations, while the APJ-shift is not robust across models, regardless of the ENSO phases. In the tropics, these experiments do not show a robust or coherent QBO influence on precipitation. The sign and spatial pattern of the precipitation response vary widely across models and experiments, indicating that any potential QBO signal is strongly modulated by the prevailing phases of the ENSO. The QBO teleconnection to the Walker circulation around boreal summer/autumn is investigated to identify the strongest signal in each model. It is found that the upper-level westerly and lower-level easterly anomalies in the equatorial troposphere over the Indian Ocean and Western Pacific are detected in the observations and most models in the La Nina year. Overall, the QBO can modulate the zonal circulation over the tropical Indian-Pacific oceans, with its impact varying depending on the ENSO phase.