Tidal heating of a solid planetary body occurs by viscous dissipation, depending on its internal structure(1-5) and thermal(5-8) and orbital(6-9) states. Calculations of the response of the Moon to tidal forces have considered lunar interior structure(1-5), but have not reproduced the geodetically observed dependence of dissipation on the lunar tidal period(10). The attenuation of seismic waves in the deep lunar interior(11,12) is expected to be consistent with a low-viscosity layer at the core-mantle boundary, which may explain the observed frequency dependence(13). Here we numerically simulate the viscoelastic tidal response of a Moon that contains a low-viscosity layer at the core-mantle boundary and compare with geodetic observations(10,14,15). In our simulations, a layer with a viscosity of about 2 x 10(16) Pa s leads to frequency-dependent tidal dissipation that matches tidal dissipation measurements at both monthly and annual periods. Compared with the lunar asthenosphere, the calculated viscosity is extremely low, and suggests partial melting at the lunar core-mantle boundary. We also find that tidal dissipation is not evenly distributed in the lunar interior, but localized within the low-viscosity layer, which implies that this layer may act as a thermal blanket(16) on the lunar core and influence the Moon's thermal evolution.