To the End of the World

Suh Hee is left by her mother at an orphanage as a small child. She grows up at the orphanage and becomes close to Sae Joon, the son of the orphanage's director. The Director objects to her son dating Suh Hee and kicks Suh Hee out of the orphanage shortly before she graduates from high school. Suh Hee must survive on her own in the outside world. Sae Joon continues to love Suh Hee despite his mother's objections.
(Source: DramaWiki)