We report the first detections of associated H i 21 cm absorption in Gigahertz-peaked-spectrum ( GPS ) sources at high redshifts , z > 1 , using the Giant Metrewave Radio Telescope ( GMRT ) . Our GMRT search for associated H i 21 cm absorption in a sample of 12 GPS sources yielded two new detections of absorption , towards TXS 1200+045 at z = 1.226 and TXS 1245 - 197 at z = 1.275 , and five non-detections . These are only the sixth and seventh detections of associated H i 21 cm absorption in active galactic nuclei ( AGNs ) at z > 1 . Both H i 21 cm absorption profiles are wide , with velocity spans between nulls of \approx 600 km s ^ { -1 } ( TXS 1200+045 ) and \approx 1100 km s ^ { -1 } ( TXS 1245 - 197 ) . In both absorbers , the large velocity spread of the absorption and its blueshift from the AGN , suggests that it arises in outflowing neutral gas , perhaps driven by the radio jets to high velocities . We derive mass outflow rates of { \dot { M } } \approx 32 { M } _ { \odot } yr ^ { -1 } ( TXS 1200+045 ) and { \dot { M } } \approx 18 { M } _ { \odot } yr ^ { -1 } ( TXS 1245 - 197 ) , comparable to the mass outflow rates seen earlier in low-redshift active galactic nuclei .