Home Secretary Amber Rudd will say those found guilty of repeatedly viewing terrorist material could face up to 15 years in jail.
The new law will extend an existing ban on downloading and possessing the content on a PC to repeatedly watching it through sites like YouTube.
Ms Rudd said: “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.
“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.”
The move comes as Ms Rudd ramped up her calls for internet giants such as Google and Facebook to do more to tackle the scourge of online extremism.
The Home Secretary yesterday criticised firms for developing encrypted software that has held back the authorities from investigating suspicious activity.