An Imperial Army is an army of any empire. However, only some empires in history and in fiction have actually referred to their armies as "The Imperial Army".
Former Imperial Armies
In Asia
The Imperial Japanese Army
The Imperial Chinese Army
The Manchukuo Imperial Army
The Imperial Korean Army
The Imperial Iranian Army
In Europe
The Imperial Roman army
The Byzantine army
The Ottoman Army
The Army of the Holy Roman Empire (until 1806)
The Army of the Holy Roman Emperor (until 1806)
The Imperial German Army (1871–1918)
The Imperial Austrian Army (1806–1867)
The Austro-Hungarian Army (1804–1918)
The Imperial Russian Army (1721–1917)
The French Imperial Army (1804–1814 and 1815)
The Swedish Imperial Army (1611–1721)
Elsewhere
The Imperial Brazilian Army
Fictional
The Imperial Army (Star Wars) of the fictional Galactic Empire in Star Wars
The Imperial Army of the Archadian Empire in the video game Final Fantasy XII
The Imperial Army of the Imperium of Man in Warhammer 40000