"Spears has recently demonstrated a level of independence that calls into question whether a conservator of the person is required," the filing said, citing the singer's hiring a lawyer of her own choosing and driving alone again.
The decision to end the conservatorship rests with Los Angeles judge Brenda Penny. The matter is due to be discussed at a hearing on Sept 29.
The "Stronger" singer was placed under the conservatorship in 2008 after suffering a public mental health breakdown. The nature of her mental health issues has never been revealed.
In late 2009, she returned to performing, recording several more albums, and going on sell-out world tours until her last performance in late 2018. The conservatorship then came under increasing scrutiny from fans in the #FreeBritney movement.
Spears, who posts frequently on her Instagram page from her mansion outside Los Angeles, did not refer to the petition by her father on Tuesday.