In this work, the normal density $rho_n$ and moment of inertia of a moving superfluid are investigated. We find that, even at zero temperature, there exists a finite normal density for the moving superfluid. When the velocity of superfluid reaches sound velocity, the normal density becomes total mass density $rho$, which indicates that the system losses superfluidity. At the same time, the Landaus critical velocity also becomes zero. The existence of the non-zero normal density is attributed to the coupling between the motion of superflow and density fluctuation in transverse directions. With Josephson relation, the superfluid density $rho_s$ is also calculated and the identity $rho_s+rho_n=rho$ holds. Further more, we find that the finite normal density also results in a quantized moment of inertia in a moving superfluid trapped by a ring. The normal density and moment of inertia at zero temperature could be verified experimentally by measuring the angular momentum of a moving superfluid in a ring trap.
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