Floods and extreme rainfall are common climatic phenomena in Bangladesh, and farm households are more susceptible to such shocks. This paper assesses the impact of climate shocks on agricultural income and food security of farm households in Bangladesh using an extensive nationally representative dataset from the Bangladesh Integrated Household Survey 2018-19, including 5604 sample rural households in 64 districts. However, this research considered 24 districts, representing 2131 sample farm households, by developing an exogenous climate shock indicator based on data from the Yearbook of Agricultural Statistics of Bangladesh 2018. Empirical findings on the grounds of simultaneous quantile regression reveal that climate shocks substantially lower agricultural income in the study regions. However, the presence of prime-age women (15-49) in the home, the male-headed family, farmland, and livestock ownership of the household are the decisive factors that safeguard agricultural income. Applying the Food Insecurity Experience Scale (FIES), descriptive statistics disclose that most farm households suffer at various food insecurity levels (considerably moderate, noticeably mild, and tiny severe), while the rest are at the food security level. The key finding regarding ordered probit regression uncovers that climate shocks significantly increase household food insecurity (at different levels of FIES). In other words, cropland damage due to floods and extreme rainfall reduces the food security of farm households in the study districts. On the other hand, increased farm size and educated households are profoundly protected against food insecurity. This study, therefore, recommends that raising livestock can complement agricultural income, and enhancing education would ensure households' food security in the climate-exposed areas of Bangladesh.