More than 1000 people applied and after all but 38 were rejected, the energy giant is appealing for more applications to fill the remaining posts.
Bosses wanted to recruit apprentices to work in Glasgow, Edinburgh and Chester. More than 30 will be based in Glasgow and all 80 will spend time at the firm's training centre in Cumbernauld, North Lanarkshire.
Although dozens of youngsters have been taken on, the Glasgow firm still needs to fill 42 apprenticeships for its engineering foundation programme. Applicants must be aged 16-19.
Human resources director Sheila Duncan was overwhelmed at the response from job hunters.
She said: "We are looking to deliver some of the biggest upgrades to the electricity network in half a century at the same time as delivering substantial investments to generate low carbon electricity.
"We need a skilled and capable workforce across the board to deliver these investments, and as part of this we need to have a focus on younger generations who will be able to manage and deliver projects over the long term."
ScottishPower plans to create 1500 jobs during the next 10 years because 80% of existing workers are set to retire by 2028.
Rail chiefs have also been inundated with job applications. ScotRail advertised for 18 trainee driver posts, created as part of the £300million Borders Railway project, and got 2229 applications.