Yamada was born in Abu District, Nagato Province (in what is now part of the city of Hagi, Yamaguchi), and was the son of a samurai official of the Chōshū Navy with a 102 koku territory.

A strong supporter of the sonnō jōi movement, he signed his name in blood (together with Takasugi Shinsaku, Kusaka Genzui, Itō Hirobumi, Inoue Kaoru, Shinagawa Yajirō) to a petition to rid Japan of the foreigners.

In June 1869, Yamada was received in an audience (together with Kuroda Kiyotaka) and appointed Hyōbu no dai-jō (senior staff officer in the Ministry of War).

In addition, he helped develop the modern Japanese legal code/ [2] During his visit to France as a member of the Iwakura Mission, he was convinced that the Napoleonic Code of "law takes precedence over the military", was necessary for Japan.

On January 28, 1892, he was appointed to a seat in the Privy Council but died in November of the same year at the age of 49, while inspecting the Ikuno Silver Mine in Asago, Hyōgo.