Scottish Power is to raise the cost of gas by 19% and the cost of electricity by 10%.
The utility firm said the increase, which would affect 2.4 million households in the UK, would come into effect from 1 August.
Affected customers will see an average daily rise to a dual fuel energy bill of 48p per day.
The company said the move reflected sustained increases in the wholesale energy market.
However, it said about 700,000 households would be protected by capped or fixed priced deals.
Watchdog Consumer Focus described the price rise as a "body blow for customers".
Scottish Power, which is part of Spanish company Iberdrola, last put its prices up in November, when gas prices rose 2% and electricity bills went up by 8.9%.
Other suppliers are widely expected to follow Scottish Power's lead over the coming weeks.
Raymond Jack, Scottish Power's UK retail director, said: "Wholesale prices for gas and electricity have increased significantly since the end of last year and continuing unrest in global energy markets means future prices are volatile.
"We understand times are difficult for many people, and we have done what we can to absorb these additional costs for as long as possible to minimise the impact on our customers."
The power company has also launched an new online product with a long fixed-price offer that it claims is one of the cheapest in the market.
Scottish Power said it could also help its customers to reduce their fuel bills by making energy efficiency savings in their homes.
Mr Jack added: "Some of our customers could save an average of £459 per year by making simple changes to the way they pay for their energy, switching to paper-free online billing and selecting one of our new or existing energy products."
Audrey Gallacher, head of energy at Consumer Focus, said: "This huge increase will be a body blow for consumers and we fear other firms will follow Scottish Power's lead.
"Companies have been softening customers up for price rises for months but customers will be shocked at the scale of this rise. Every household in the country will now be bracing themselves for impact.
"When this affects the cost of keeping warm and well, it is not an acceptable state of affairs."
Energy regulator Ofgem recently called for the industry to be overhauled after it found that the "big six" companies had put up prices more quickly than they reduced them when costs fell.
A separate inquiry has been launched into Scottish Power's pricing plans.
Scottish Power's latest rise will mean that customers who take gas and electricity from the company but pay quarterly by cash will see their annual bills rise by an average of £180 to £1,391.