The vaccination is given via a nasal spray into each nostril, rather than a needle. It is quick and painless, and the best available protection against flu.
However, uptake is low nationally this year and health leaders in Wolverhampton are keen to ensure that youngsters in the city are protected this winter.
Councillor Jasbir Jaspal, the City of Wolverhampton Council's Cabinet Member for Public Health and Wellbeing, said: "If your child is aged 2 or 3, please book their flu vaccination with your GP as soon as you can.
"Flu is not only highly infectious but the virus can cause serious illnesses in children, such as bronchiolitis and pneumonia, so it's better to be safe than sorry."
Sally Roberts, Chief Nursing Officer for the NHS Black Country Integrated Care Board, added: “The flu virus is a highly infectious respiratory virus that can spread very quickly among children.
“Vaccinating your child will not only help protect them from getting flu but also prevent it from spreading to other children, as well as vulnerable family members and friends. The vaccine is quick and painless, and is proven to be extremely effective against flu."
Flu vaccinations via the nasal spray are also being offered to school children from Reception to Year 9 again this year.
The vaccination is available by injection if parents do not wish their child to have the nasal spray, or if children are unable to have it for medical reasons, for instance if they have a supressed immune system or severe egg allergy.
To find out more about the flu vaccine for children, read the answers to frequently asked questions and to download or watch the 4 exciting Flu Fighters stories for children, Flu Fighters Versus Chilly, Achy and Snotty, Flu Fighters in The Battle of Planet Bogey, Flu Fighters in Close Encounters of the Germed Kind and Flu Fighters on a Vacc-tastic Voyage, please visit Flu Vaccines.