Anayama Nobuyoshi was a bushi and second son of Anayama Nobutomo.
In 1565, the eldest son of Takeda Shingen, Takeda Yoshinobu, was imprisoned on charges of plotting a rebellion, an event known as the Yoshinobu Incident. His guardian, Obu Toramasa, was forced to commit seppuku after being found implicated in the plot. Yoshinobu wed the younger sister of Imagawa Ujizane, lord of the Imagawa clan. This arrangement, along with other political marriages between the clans, provided a foundation for the peace accord among the Takeda of Kai, the Hōjō of Sagami, and the Imagawa of Suruga in 1554. This alliance was known as the Kōsōsun sangoku dōmei. The Anayama of Kai maintained a deep relationship with the Imagawa in neighboring Suruga Province, serving as diplomatic intermediaries for the Takeda and Imagawa. Nevertheless, the Yoshinobu Incident caused a souring of relations between the clans. In 1568, the Takeda abandoned the three-party alliance, severed ties with the Imagawa, and launched an attack in Suruga.
Prior to these developments, in 1565, there may have been a split within the Takeda clan, with Yoshinobu in favor of maintaining the alliance while Shingen and his supporters opposed it. Anayama Nobutada sided with Shingen, while Nobuyoshi aligned himself with Yoshinobu, leading to his imprisonment after the Yoshinobu Incident. In 1567, Nobuyoshi killed himself in a building for the commemoration of priests at the Kuon Temple run by adherents of the Nichiren sect of Buddhism.