Climate change inevitably affects the deterioration of reinforced concrete (RC) bridges exposed to harsh chloride environments. This deterioration reduces the resistance of RC bridges to natural hazards, including earthquakes and floods. This paper proposes an improved framework for time-dependent multi-hazard seismic vulnerability and risk assessment of a deteriorating RC bridge considering climate change. The framework addresses (a) the corrosion initiation and propagation processes affected by climate change, (b) time-dependent corrosion rate, (c) seismic fragility analysis of a deteriorating RC bridge using a three-dimensional finite-element model, and (d) the integration of deterioration due to corrosion, climate change, and earthquake and flood-induced scour hazards into time-dependent seismic vulnerability and risk assessment. This paper provides extensive comparisons to demonstrate the effects of corrosion propagation based on uniform and pitting corrosion models, climate change, intensity of ground motion of earthquakes, and flood-induced scour on seismic vulnerability and risk. For illustration, an existing multi-span RC girder bridge is investigated. The results show that pitting corrosion under climate change with flood-induced scour significantly increases the seismic vulnerability and risk of deteriorating RC bridges.