Born in Zemun, Syrmia, Austrian Empire, Moser was the son of a winegrower and smoker from Upper Austria.
In addition to his studies, he gained further musical experience, among other things as first violinist of the "Zurich Student Quartet" and conductor of the Stuttgart Academic Singing Association.
He finally turned his attention to music for good and in 1878 became a student of Joseph Joachim at the Berlin University of the Arts.
Among his students were Pálma von Pászthory, Josef Wolfsthal, Robert Imandt, Richard Czerwonky, Hans Bassermann and Julius Ruthström.
However, he suffered from a "nervous complaint of the arm" (E. van der Straeten), which prevented him from performing regularly, so he concentrated on teaching.