Pressure comes from a combination of population growth, changes in care and treatment for critically sick and injured children, and the increasing complexity of cases.
About 1200 children are admitted to the Starship PICU every year.
"We can do so much more, and the things we can do now mean that children survive, who might not otherwise," said Beca.
Starship is part way through designing a new expansion that will add 10 intensive care beds by winter 2022.
Over the next two to three years, the project will also build more support spaces for whānau and staff, and a medical day stay unit for children who do not need to stay overnight.
The project will cost $40m, of which the Government has committed $25m.
Starship Foundation is working to raise the extra $15m and has already secured $7m in pledges and donations, says foundation chief executive Aisha Daji Punga.
"Our nurses and clinicians can fix many things but they can't fix a shortage of beds.
"We urgently need the help of generous New Zealanders to make this happen," she said.
Donations can be made online at www.starshipicu.org.nz.