Believed to have been born around 1140 in Hirayama, Musashi Province (present-day Hino). A member of the Himatsuri clan within the Nishito faction of the Musashi Shichito, he took the name Hirayama from his home fief. After Minamoto no Yoritomo raised his army, Sueshige joined his forces as a gokenin and served under Minamoto no Yoshitsune during the Genpei War. At the 1184 Battle of Ichinotani, he reportedly joined a surprise assault, breaking into Taira lines alongside Kumagai Naozane to help secure victory, and he fought at the front again at Yashima and Dan-no-ura the following year. He is thought to have died around 1212.

Known for his fearless valor even when outnumbered, he is remembered as a fierce warrior who repeatedly led the charge across the battles of the Genpei War.

Sueshige's home fief of Hirayama survives as a place name in present-day Hino. Within Hirayama Castle Ruins Park, believed to be the site of his residence, a shrine dedicated to him still stands. Hino City continues to honor him today as a local warrior of the Kamakura shogunate era.