The premise of Potato Star starts with Na Jin-ah (Ha Yeon-soo) and her mother Gil Sun-ja (Oh Young-sil). They live in a shabby house on the outskirts of Seoul. Jin-ah dreams of working in Kong Kong, a toy company who's origins also involves her late father. Despite her father's contributions to the now large corporation, the family only receives one bag of rice a year.
One day, a young man that goes by the name of Hongberg (Yeo Jin-gu) moves in to the old house next door. The house is basically abandoned, so he often visits the Na family for basic needs like bathroom, food, and electricity. Meanwhile, Kong Kong's president, Noh Soo-dong (Noh Joo-hyun) decides to retire. His son, Noh Min-hyuk (Go Kyung-pyo), an arrogant Harvard graduate, takes over the company. His somewhat nontraditional approach gains him a few enemies. On the other hand, his new policies would grant Jin-ah her entrance to the company.
Suddenly, a potato-like meteor strays off its predicted course, possibly crashing to earth itself. This brought chaos to the world, and a few changes to the lives of our characters.