The coast of south-western Bangladesh has been facing an increasing severity of climate stressors, thereby affecting the livelihoods of households. This has necessitated the importance of understanding the complex aspects of their sustainability. This study investigates factors influencing household income and livelihood sustainability of coastal residents in southwestern Bangladesh. A survey was carried out among 300 heads of households from the Kailashganj and Laudubi villages under Dacope sub-district of Khulna district (a climate-sensitive region) in Bangladesh. We utilized the composite livelihood sustainability index (LSI) and multiple linear regression to identify the factors influencing coastal households’ income. Findings revealed that the overall LSI among the households was 0.663 (moderate sustainability). Additionally, the highest LSI was found in terms of social capital and the lowest LSI was identified in terms of financial capital. The findings of the regression analysis indicated that monthly household income was positively and significantly influenced by its close linkages to local leaders (p < 0.05) and association with non-governmental organizations (p < 0.01). Moreover, economically active members (p < 0.01), more accessibility of commuting transportation (p < 0.01), and availability of water for irrigation (p < 0.01) were positively and significantly derived the monthly household income. Policymakers can use these results as a basis for formulating policies (e.g., enhancing the training and skill development programs as well as prioritizing investment in expanding irrigation systems) that can address the essential livelihood and income requirements of the community that is affected by climate change.