Coming to a new country involves many challenges. One of them is to approach a new health care system when you have a child with asthma. The aim of this study was to gain a broader understanding of immigrant parents’ experiences of the Swedish health care system. Twelve parents of children with asthma were interviewed and their narratives were analyzed by using qualitative content analysis. The results show that immigrant parents’ experiences of Swedish health care vary and involve both advantages and disadvantages. Advantages of the Swedish health care system are described as Being met with respect and Affordable care, while disadvantages are described as Problems with communication, Being discriminated against and Lack of confidence. The disadvantages are challenges for health care professionals, who are expected to offer care on equal terms to the whole population. Therefore, they need to provide culturally competent care and encourage immigrant parents to voice their expectations and worries.