The company will raise standard tariff electricity prices by 10.8% from 31 March, while gas prices will increase by 4.7%.
It means a typical dual fuel annual bill will rise by an average of 7.8%, or Â£86.
Scottish Power said in a statement that about a third of its customers - or about 1.1 million homes - would be affected by the increases.
It attributed the move in part to rises in energy wholesale markets and compulsory non-energy costs, including the upgrade to smart meters.
Scottish Power's announcement came as British Gas said it would extend a price freeze for its customers on its standard energy tariff until August.
Last month, Npower faced a backlash after it said it would raise standard tariff electricity prices by 15% from 16 March, and gas prices by 4.8%.
Scottish Power's UK retail director, Colin McNeill, said: "This increase will apply to one in three of our customers, and we continue to work hard to move even more customers to our fixed price deals.
"We will be writing to all those affected, outlining the changes and encouraging more loyal customers to move to a deal that best suits them.
"This price change follows months of cost increases that have already led to significant rises in fixed price products that now unfortunately have to be reflected in standard prices."
Scottish Power has announced a sharp increase in energy prices.