In 1993, Steinberg appeared in the series Der Fahnder and from this time on appeared in series such as Ein starkes Team, Marienhof, Die Rosenheim-Cops, SOKO 5113 and Sturm der Liebe, as well as in movies for TV and cinema.
In the film Downfall, he played the short role of General der Flieger Karl Koller.
Steinberg is also active as a stage actor, in the season 2009/2010 his role in Schiller's drama The Robbers was Maximilian von Moor.
In the summer of 2014, Hans H. Steinberg participated in the Störtebeker Festival in Ralswiek on the island of Rügen.
Steinberg lives in Munich and speaks fluent German and English.