Magnetospheric convection is a fundamental process in the coupling of the solar wind, magnetosphere, and ionosphere. Recent studies have shown that dayside magnetopause reconnection drives magnetospheric convection, progressing from the dayside to the nightside within approximately 10–20 min in response to southward turning of the interplanetary magnetic field. In this study, we use global magnetohydrodynamic (MHD) simulations to investigate the influence of ionospheric conductance on dayside‐driven convection. We conduct three simulation runs: two with normal ionospheric conductance and one with nearly infinite conductance. The temporal and spatial pattern of magnetospheric convection largely remain consistent across all three simulation runs. Comparing the results, we observe a reduction of 20% in magnetospheric convection and a 30% increase of ionospheric Region 1 field‐aligned current (FAC) and Pedersen current in the run with nearly infinite conductance, compared to the normal conductance model. The results indicate that ionospheric conductance does not affect the response time of enhanced magnetospheric convection to the solar wind. We suggest that the 10–20 min timescale for establishing magnetospheric convection corresponds to the anti‐sunward drag of reconnected magnetic field lines from the sub‐solar point to the flank magnetopause. In cases of larger ionospheric conductance, the ionosphere footprints of dragged field lines become more stationary, potentially resulting in larger Region 1 FAC and ionosphere Pedersen current. A larger Pedersen current is associated with stronger sunward J × B force in the ionosphere, which corresponds to a stronger anti‐sunward force in the magnetosphere, thereby reducing sunward convection of closed field lines.