We have determined the frequency dependence of anelastic attenuation for both P and S waves in the upper mantle of the moon in the frequency range of roughly 3 to 8 Hz. The method used is a combination of a single-station method, in which Q-1 is obtained as an integral with an unknown constant, and a multiple-station method, the result of which is used to determine the integration constant. The Q determined for P waves (Qp) appears to decrease with increasing frequency, through it is not significantly different from a constant Q, while the Q for S waves (Qs) increases with frequency, becoming significantly greater than Qp at high frequencies. All Q values remain greater than 4000 within this frequency range. Qs above 5 Hz is approximately proportional to the 0.7th power of frequency. The high Q for shear waves at high frequencies suggests that compressional heat loss may be a dominant dissipation mechanism. Some uncertainites in the absolute Q values remain because the detailed velocity structure of the lunar upper mantle is largely unknown.