For many developed countries and regions, long-term care is becoming an important issue due to demographic changes and an increasing willingness and need of family members to let the elderly be taken care of by non-family members. Thus, effectively managing long-term care needs has become a major societal concern. In this paper, the public attitude towards long-term care and the satisfaction of long-term care services in Taiwan are examined. First, internal consistency reliability, exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) are applied to delete unimportant indicators. Second, structural equation modeling (SEM) is used to determine which indicators have a statistically significant influence on the public attitude toward long-term care and on the satisfaction of long-term care services. Third, artificial neural network (ANN) is applied to understand the relative importance of the indicators in influencing the public attitude and satisfaction of long-term care services. The contribution of this study is significant because some of the factors investigated in the study should be stressed by the government or institutions to provide more satisfactory services to the elderly and their families.