This paper proposes a velocity observer for caster wheel odometers resisting steady-state error. The proposed method is established by attaching a feedback loop of error integration to extended Luenberger observer (ELO). The stability of the proposed observer is proved, moreover, the steady-state error converges to a bounded area where the bounds are defined by design parameters. This fact guarantees that the proposed method is robust against a certain class of model error as well as measurement noise. The advantage over the simple ELO or the conventional approximated differentiator is verified in numerical simulations and experiments.