The invention provides a high-damping Mn-Cu damping alloy and a manufacturing method thereof. The alloy comprises chemical components of: 60.00-75.00 wt% of 2.00-5.00 wt% of Ni, 0.50-3.00 wt% of Al, 1.50-2.50 wt% of Fe, no more than 0.01 wt% of C, no more than 0.10 wt% of Si, less than 0.020 wt% of P, less than 0.020 wt% of S, no more than 0.050 wt% of N, no more than 0.010 wt% of O, one or more selected from Zr, Ti, La, Ce, Y and mixed rare earth (Mm), and the balance of Cu and inevitable impurities. After heat treatment, the alloy has damping performances as follows: Q<-1><max> of 0.035-0.055, Q<20 DEG C> <-1> of 0.020-0.040, and Q<110 DEG C> <-1> of 0.010-0.030. The alloy has high damping capacity, good temperature stability, wide temperature range, high strength and good processability, can be processed into sectional material and strips, is applicable to the parts requiring vibration and noise reduction in the fields of aviation and space flight, navigation, nuclear industry, automobile manufacturing, electrical equipment and precision instruments and instrumentation, and can play the roles of reducing the vibration transmission, reducing noise and prolonging the service life of structural components.