People who repeatedly view terrorist content online will face up to 15 years in prison, the home secretary is to tell the Conservative Party conference.
Amber Rudd will set out her intention to change the law to increase the maximum penalty from 10 years.
The offence of possessing information likely to be useful to a terrorist will also apply to material viewed repeatedly or streamed online.
Currently it applies only to material that is downloaded and stored.
The terms of the new offence will be designed safeguard those who click on a link by mistake, or who could argue that they did so out of curiosity rather than with criminal intent.
'Despicable'A defence of "reasonable excuse" would still be available to academics, journalists or others who may have a legitimate reason to view such material.
The new 15-year sentence would also apply to those who publish information about members of the armed forces, police or intelligence services for the purposes of preparing acts of terrorism.
"I want to make sure those who view despicable terrorist content online including jihadi websites, far-right propaganda and bomb-making instructions face the full force of the law," Ms Rudd said.
Streaming is becoming an increasingly common way for criminal and extremist material to be viewed online and there is a "gap" in the law as it stands, she said.
"Changes will enable police and the security service to keep pace with modern patterns of internet use and intervene earlier in an investigation given the speed with which online radicalisation is taking place."
She also said the government was continuing to "urgently press" internet companies to do more to stop such material being available on their platforms in the first place.
It comes a day after Ms Rudd accused technology experts of "patronising" and "sneering" at politicians who tried to regulate their industry.
Speaking at a Spectator fringe meeting in Manchester, Ms Rudd said Silicon Valley had to do more to help the authorities access messages on end-to-end encrypted services such as WhatsApp.
And she said she did not need to understand how they worked to know they were "helping criminals".