Just under 50 believers chanted slogans and held banners calling on judges to treat them the same as Muslims in civil cases.
They claimed the courts have a bias towards Islam and will normally believe a Muslim over a Christian.
It was a rare show of defiance to the state from Christians, as protests like this are banned in the country.
It passed peacefully but police ordered the group to disperse after an hour.
Michael Armanious told AP: "I am an Egyptian citizen above all, we pay taxes, we serve in the army, we are dealing with all the same economic problems in Egypt with the rest of our countrymen, why should we have fewer rights."
There's been an increase in violence against Christians in Egypt in recent months.
In May an elderly Christian woman was stripped and left naked in the street of her village by a mob of Muslims.
The group also destroyed seven homes after rumours that a Christian man was having an affair with a Muslim woman.
At the start of August a video appeared online showing a mob attacking Christians and their homes in northern Egypt.
The footage showed the gang throwing stones, breaking glass and chanting in Saft al-Kharsah village in Beni Suef Province, near Cairo.
Rumours that a man's home was being turned into a church were said to have angered the Muslims who decided to attack the village.
