Asim Omer, who was studying at Khartoum University, was arrested in December last year and charged with killing the policeman after hundreds of students clashed with security forces at the campus on the banks of the Blue Nile in April 2016.
Last month the court found Omer guilty, and today sentenced him to be hanged.
"The judge sentenced Asim Omer to be hanged to death after finding him guilty of killing a policeman," defence lawyer Mohamed Arabi told AFP, adding he would appeal.
Students at Khartoum University several times last year demonstrated against what they said was a plan to sell off buildings belonging to the institution.
The government denied the charge, and police often resorted to firing teargas to disperse the protesters.
Demonstrations against local grievances occur frequently in Sudan but are often suppressed by police and state security agencies.
In late 2016, sporadic anti-government rallies were staged in Khartoum after the government raised fuel prices.
The demonstrations were swiftly broken up by security forces, and dozens of opposition leaders and activists were arrested.
Thousands of people took to the streets of Khartoum and in some other regions calling for the downfall of President Omar al-Bashir's regime, also after the authorities slashed fuel subsidies.
Rights group Amnesty International said at the time that about 200 people were killed, hundreds were wounded and more than 800 arrested.
The government gave a death toll of fewer than 100.
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