The tenth of twelve children, he spent his young childhood in his native Hrotovice and 1845 went to Znojmo for secondary school.
He accepted a position teaching drawing in a higher secondary school in Kutná Hora, where on July 15, 1863, he married Jindřiška Janečková.
Zvěřina died after a severe illness on 27 December 1908 in Vienna, Austria, and was buried in the Central Cemetery.
The topics of his artwork drew mainly from his places of residence in Maribor, Gorizia, Old Herzegovina and Montenegro.
During his life he held many exhibitions in Prague, Brno Budapest, Vienna, Kraków, and elsewhere.