The Round's 5.7-inch display, made from flexible materials, is curved along the vertical axis, curving from left to right.
The screen's shape allows the entire device to be curved, a feature intended to provide a comfortable hand grip feeling to the user, Samsung said in a release.
Other than the shape, the smartphone's specifications are nearly identical to Samsung's Galaxy Note 3 introduced last month.
The Round runs the Android 4.3 operating system with Samsung's own TouchWiz enhancements.
So far, the Round is only available in South Korea at a price of $1,000. Samsung has not said whether or when other markets would get the curved device.
South Korean competitor LG has announced a curved-screen smartphone, expected next month.
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