Kalju Kivi first studied in Tartu and Otepää. He then attended vocational school to become a locomotive driver's assistant. Later, Kivi studied wood processing at the Tartu Art School and fashion art at the Estonian Art Institute.
In 1980, he started working at Tallinnfilm. He worked as a director, artist, and screenwriter for puppet films. Kalju Kivi created over ten animated films, including "The Adventures of a Sheet of Paper", "The Baker and the Chimney Sweep", "The Knot", "Ascent", and "Humachinoid".
From 1994 onwards, he worked at the Estonian Puppet Theatre. He was an artist there and later became the chief artist. He created designs for nearly 20 productions, such as "Friend Cucumber", "Risk", "Timbu-Limbu and the Snow Trolls". In addition to the Puppet Theatre, he also created designs for the Endla and Polygontheatres.
Kalju Kivi designed sets for 18 feature films. He collaborated with directors such as Elmo Nüganen, Peeter Simm, and AJ Annila. Their films include "Names in Marble", "1944", "Georg", and "Itkitie".
He also created designs for museums and exhibitions. For example, for Rakvere Castle, Paide Vallitorn, and Palmse Manor. He contributed to the Lottemaa exhibition and the "BACK to the ACTION" exhibition.
Kalju Kivi began working in television as a student. He created children's programs like "Saturday with Dad" and "The Workshop". Since 2012, he worked as a freelancer. He was also a member of the board of the company "KIVI & KIVI".
In 2004, Kalju Kivi received the Order of the White Star, Fifth Class. Twelve years ago, he was diagnosed with cancer.
Kalju Kivi's works can be viewed in the ERR archive. There are programs such as "Echoes. Kalju Kivi" (2018) and "The Workshop" (1988). In the latter, Kivi taught how to do woodwork. The program discussed hand tools and techniques.