Background Parental satisfaction is a key measure of the quality of a child's anesthetic care. Understanding of parents' opinions and satisfaction about their child's anesthesia service in the hospital is vital for hospital funding and parent experience. Objective The purpose of this study was to determine the level of parental satisfaction with their child's anesthetic care and the factors that contributed to that satisfaction. Methods An institution-based cross-sectional study was undertaken between March and June 2021. A structured questionnaire with the background characteristics of parents and children was used to collect data. A total of 238 parents were included in the study. To find parameters linked to parental satisfaction with their child's anesthetic service, bi-variable, and multi-variable logistic regression analyses were used. Crude odds ratio and adjusted odds ratio with a 95% confidence interval (CI) were estimated. Variables with a p-value < 0.05 were considered statistically significant in multivariable analysis. Result The proportion of parental satisfaction toward their child's anesthesia service was 77.7% (95% CI: 72.3, 82.4%). Non-anxious, male, employed, and urban resident parents and parents of pre-medicated children were associated with high satisfaction scores. Conclusion and Recommendation Overall, parents' satisfaction with their child's anesthesia service was promising. Parents who were non-anxious, male, employed, and lived in an urban area and whose child had received sedative premedication had high rates of parental satisfaction with their child's anesthetic care. Parents from rural areas, as well as worried and female parents, should receive extra care. Preoperative anxiety is reduced when parents are given enough and understandable information. Thus, the provision of comprehensive information on their child's anesthesia care process and psychological or emotional support to parents are necessary to boost their satisfaction.