Six new episodes are being made, to follow on from the pilot episode, which was shown on BBC Two in April 2020.
The cast returning for the full series alongside Willan, who plays the lead character Alma Nuthall, are: Siobhan Finneran as her mum, Lin; Lorraine Ashbourne as her nan, Joan; Jayde Adams as her best friend, Leanne; James Baxter as Alma's ex-boyfriend, Anthony; and Nicholas Asbury as Jim.
Filming on the series began in Bolton at the end of April, with the episodes expected to be broadcast on BBC Two later this year.
The BBC says: "The series follows Alma as she tries to get her life back on track after a break-up. But with no job, no qualifications and a rebellious streak a mile wide, it's not going to be easy. Meanwhile her mum, who is battling a heroin addiction, has been sectioned for arson and her vampish Grandma Joan wants nothing to do with it. Alma's Not Normal offers a bitingly funny and unflinching take on class, sexuality, mental health and substance abuse. It celebrates women dealing with the hands they've been dealt while doggedly pursing their dreams."
Sophie Willan - who is nominated for a BAFTA for her writing on the pilot - says: "I'm delighted that filming is underway for Series 1 of Alma's Not Normal, and even happier to be working alongside such a fantastic group of actors! We can't wait for audiences to learn more about Alma's world and the eclectic mix of characters that surround her."
Nerys Evans, executive producer at production company Expectation, comments: "We're delighted to be making a full series of Alma's Not Normal, after such a wonderful response to the pilot. Sophie is an incredible talent - she is such a gifted writer and performer and has written something that feels both utterly modern and yet timeless. With Gill Isles producing and Andrew Chaplin directing, we have an extraordinary team around Sophie to bring Alma to life."