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We have observed the Fano-Kondo anti-resonance in a quantum wire with a side-coupled quantum dot. In a weak coupling regime, dips due to the Fano effect appeared. As the coupling strentgh increased, conductance in the regions between the dips decreased alternately, showing the growth of the Kondo state. From the temperature dependence and the response to the magnetic field, we conclude that the conductance reduction is due to the Fano-Kondo anti-resonance. At a Kondo valley with the Fano parameter $q \approx 0$, the phase shift at a quantum dot stays constant over the range of gate voltage where the system is close to the unitarity limit.

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