The Galaxy Round will feature a 5.7in display.
The launch comes just days after rival LG said it would begin production of curved-screen phones next year.
Digital display technology has been progressing towards curved screens. Both Samsung and LG already offer curved organic light-emitting diode (OLED) television sets.
Samsung Electronics said the curved screen display would help consumers use some of the features on the phone, including those that enable users to check information such as date, time and missed calls when home screen is off, with more ease.
At the same time, users can also change music tracks on their phone, even while its display is off.
The Galaxy Round will initially be launched only in South Korea. The firm gave no indication of its plans for a global launch.
The global smartphone market has been growing rapidly.
According to research firm CCS Insight, worldwide smartphone sales will hit nearly 1 billion in 2013 – accounting for more than half the total of 1.7 billion mobile phones sold.
As result, smartphone manufacturers have been keen to offer new products to win consumers.
With display technology moving towards flexible and bendy screens, it is one area that companies have been looking at.
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