The 29-minute video purports to show militants holding two groups of captives, described in a text on the screen as "followers of the cross from the enemy Ethiopian Church".
A masked fighter in black brandishing a pistol makes a statement threatening Christians if they do not convert to Islam.
The video then switches between footage of one group of about 12 men being beheaded by masked militants on a beach and another group of at least 16 being shot in the head in a desert area.
Before the killings, the video shows purported footage of Christians in Syria explaining how they had been given the choice of converting to Islam or paying a special tax, and had decided to pay.
The video bore the logo of IS's media arm and was similar to footage released in the past, including of a group of 21 Coptic Christians, mainly Egyptians, beheaded on a Libyan beach in February.
Several Libyan jihadist groups have pledged allegiance to IS, the extremist organisation that seized control of large parts of Syria and Iraq last year and declared an Islamic "caliphate".
The country has been wracked by unrest since the 2011 uprising that toppled and killed dictator Moamer Kadhafi, with two opposing governments and armed groups battling to control its cities and oil wealth.
UN-backed efforts to form a national unity government have made little progress and officials have warned that Libya -- awash with weapons after Kadhafi's overthrow -- threatens to become a haven for jihadists on Europe's doorstep.
IS has persecuted minorities including Christians and its executions of the Egyptian Copts prompted retaliatory air strikes from Cairo.
A US-led coalition of Western and Arab nations is carrying out an air war against IS in Syria and in Iraq, where pro-government forces have managed in recent months to retake some territory seized by the group.
The group's attacks have raised fears for Christians across the Middle East and been condemned by religious leaders.
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