Our aim is to measure the interstellar ^14^N/^15^N ratio across the Galaxy, to establish a standard data set on interstellar ammonia isotope ratios, and to provide new constraints on the Galactic chemical evolution. The (J,K)=(1,1), (2,2), and (3,3) lines of ^14^NH_3_ and ^15^NH_3_ were observed with the Shanghai Tianma 65m radio telescope (TMRT) and the Effelsberg 100m telescope toward a large sample of 210 sources. One hundred fourty-one of these sources were detected by the TMRT in ^14^NH_3_. Eight of them were also detected in ^15^NH_3_. For 10 of the 36 sources with strong NH_3_ emission, the Effelsberg 100m telescope successfully detected their ^15^NH_3_(1,1) lines, including 3 sources (G081.7522, W51D, and Orion-KL) with detections by the TMRT telescope. Thus, a total of 15 sources are detected in both the ^14^NH_3_ and ^15^NH_3_ lines. Line and physical parameters for these 15 sources are derived, including optical depths, rotation and kinetic temperatures, and total column densities. ^14^N/^15^N isotope ratios were determined from the ^14^NH_3_/^15^NH_3_ abundance ratios. The isotope ratios obtained from both telescopes agree for a given source within the uncertainties, and no dependence on heliocentric distance and kinetic temperature is seen. ^14^N/^15^N ratios tend to increase with galactocentric distance, confirming a radial nitrogen isotope gradient. This is consistent with results from recent Galactic chemical model calculations, including the impact of superasymptotic giant branch stars and novae.