Bobbi-Anne McLeod, 18, left her home in Leigham at around 6pm on Saturday evening and had been due to catch a bus into the city centre to meet friends.
She never arrived, and officers from Devon and Cornwall Police have urged her to contact them.
Officers have been conducting searches and inquiries across Plymouth, the force said, supported by a police helicopter.
Ms McLeod is described as having brown hair and green eyes, and was wearing a grey Nike jumper, black ripped jeans and Nike trainers.
A Facebook page set up to help find her has now attracted more than 10,000 members.
Detective Inspector Matt Lawrence said: “Bobbi-Anne McLeod was last seen leaving her home in Leigham at around 6pm on Saturday 20 November.
“We believe she was due to get a bus from Sheepstor Road into the city centre to meet some friends, but she didn’t show up.
“Bobbi-Anne is 18 years old, 4ft 11in tall and of slight build. She has brown hair, green eyes with straight shoulder-length hair and ear piercings. She was believed to be wearing grey Nike jumper, black ripped jeans and fishnet tights, and light Nike trainers.”
DI Lawrence continued: “We would like to hear from anyone who has seen Bobbi-Anne since she left her home on Saturday, or from anyone who knows of her current whereabouts.
“Bobbi-Anne may be reading this appeal, if you are then please get in touch; you are not in trouble, we just need to know that you are safe and well.”
Anyone who may have seen Ms McLeod is asked to contact Devon and Cornwall Police on 101 quoting reference 879.