Ante Kostelic, who, with his wife Marica, had been a top national handball player in the former Yugoslavia, established a demanding skiing regimen for his children when they were small. If others trained four hours a day, Janica and brother Ivica worked eight. If a typical practice consisted of skiing through 400 gates, Janica skied through 1,200. When war ripped their country in the early 1990s, the Kostelics fled their home in Zagreb and sought out training sites in Central and Eastern Europe. They had little money. When Janica and Ivica began skiing competitively, the family drove from race to race, camping in tents along the way. When the weather turned cold, they slept in the car. They often ate sandwiches for every meal. Once, they took shelter in a cave for a week because they feared air strikes. "For 10 to 12 years we never stopped," Ante Kostelic told the New York Times. "Maybe we did not know better. We did what we thought was right."
Janica entered twenty-two junior races during the 1996-97 season. She won them all. "Despite that impressive record," Time International reported, "in her first World Cup season, 1998-99, her third place in a slalom event at Park City, Utah, took officials by surprise. They couldn't find a Croatian flag for the award ceremony and Janica had to dig one out of her ski bag."