Background: Due to rapid socioeconomic development and epidemiological transition, socioeconomic inequality of underweight, overweight, and obesity are becoming a public health concern in Bangladesh. There is a need for country-specific evidence of nutrition inequalities in Bangladesh. Aim: The aim of the study was to measure socioeconomic inequality and decomposition analysis along with the sex differences in underweight, overweight, and obesity among the adult population. Methods: A secondary data analysis was performed in the Bangladesh Demographic and Health Survey (BDHS) 2017–18, a cross-sectional survey used a multi-stage cluster sampling technique. Sociodemographic variables including age, sex, education, socioeconomic status, marital status, and anthropometric data of height and weight were considered for analysis. Body mass index was used for defining underweight, overweight, and obesity. Concentration index (CI) and decomposition analysis were performed for underweight, overweight, and obesity. Results: The proportion of underweight was 15.0%, overweight (23.0%), and obese (5.0%). Underweight was higher in males, whereas overweight and obesity were higher in females. The CI of underweight was −0.121 ( p < 0.001), indicating socioeconomic inequality concentrated on lowering socioeconomic status; living in rural areas contributed 14.2% to this inequality. The CI of overweight and obesity was 0.213 ( p < 0.001) and 0.142 ( p < 0.001), respectively, indicating that inequalities of overweight and obesity concentrated in higher socioeconomic status; urban residency contributed 14.1% and 18.0% to socioeconomic inequality of overweight and obesity. Conclusion: Underweight remains a significant problem for poor people in rural areas, but overweight and obesity were highly prevalent in the higher socioeconomic status of urban areas. Education level and young age group significantly contribute to the socioeconomic inequality of malnutrition. A more detailed epidemiological study is required to understand the causes of socioeconomic disparities of nutritional status in Bangladesh.