Atiqullah Raufi, head of secretariat for the court, was gunned down as he left his home to head to work.
The Taliban have often targeted Afghan officials as well as NATO soldiers, foreign compounds and military convoys.
A spike of attacks in recent weeks have heightened concern about stability as NATO readies to end its combat mission on December 31 after a war that has failed to thwart the Taliban insurgency.
“Around 9:00 am, unknown gunmen shot dead Atiqullah Raufi as he was heading to work,” Kabul police spokesman Hashmat Stanikzai told AFP.
Taliban spokesman Zabihullah Mujahid in a text message sent to the media claimed responsibility for the killing.
On Thursday, a Taliban suicide bomber blew himself up among the audience at a French Cultural Centre in Kabul, killing one German national and wounded 15 others.
Hours earlier, another suicide bomber targeted a bus carrying Afghan troops in the suburbs of the city, killing six soldiers.
Other recent targets have included a female Afghan member of parliament, a British embassy convoy and a three members of South African family killed when their compound was attacked.
After NATO’s combat operations end, a follow-up mission of about 12,500 NATO troops will stay on in Afghanistan to train and support the local security forces now responsible for fighting the Taliban. -AFP