We present the results of a search for ammonia maser emission in 119 Galactic high-mass star-forming regions (HMSFRs) known to host 22\,GHz H$_2$O maser emission. Our survey has led to the discovery of non-metastable NH$_3$ inversion line masers toward 14 of these sources. This doubles the number of known non-metastable ammonia masers in our Galaxy, including nine new very high-excitation ($J,K$) = (9,6) maser sources. These maser lines, including NH$_3$ (5,4), (6,4), (6,5), (7,6), (8,6), (9,6), (9,8), (10,8), and (11,9), arise from energy levels of 342 K, 513 K, 465 K, 606 K, 834 K, 1090 K, 942 K, 1226 K, and 1449 K above the ground state. Additionally, we tentatively report a new metastable NH$_3$ (3,3) maser in G048.49 and an NH$_3$ (7,7) maser in G029.95. Our observations reveal that all of the newly detected NH$_3$ maser lines exhibit either blueshifted or redshifted velocities with respect to the source systemic velocities. Among the non-metastable ammonia maser lines, larger velocity distributions, offset from the source systemic velocities, are found in the ortho-NH$_3$ ($K=3n$) transitions than in the para-NH$_3$ ($K ones.