"For eight years Russia 'ran over' President Obama, got stronger and stronger, picked-off Crimea and added missiles. Weak!" the President tweeted.
In earlier tweets, Mr Trump claimed without evidence the Obama administration was responsible for 122 "vicious prisoners" released from Guantanamo Bay returning to the battlefield.
It is not the first time Mr Trump has accused Mr Obama of allowing Russia to take Crimea.
"Crimea was TAKEN by Russia during the Obama Administration. Was Obama too soft on Russia?" the US president tweeted last month.
It came as Russia insisted it did not intend to return Crimea to Ukraine after the White House said Mr Trump expected the annexed Black Sea peninsula to be returned.
Moscow said an overwhelming majority of Crimeans voted to become part of Russia in a 2014 referendum wanting protection from what the Kremlin cast as an illegal coup in Kiev.
However, Ukraine said the referendum was a sham held at gunpoint after Russian troops illegally annexed the peninsula, that Russia-friendly president Viktor Yanukovych was ousted by people power, and that Moscow should return Crimea.
The 2014 annexation prompted the United States and the European Union to impose sanctions on Russia, plunging Western relations with the Kremlin to their worst level since the Cold War.
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