In Bangladesh, major floods are frequent due to its unique geographic location. About one-fourth to one-third of the country is inundated by overflowing rivers during the monsoon season almost every year. Calculating the risk level of river discharge is important for making plans to protect the ecosystem and increasing crop and fish production. In recent years, several Bayesian Markov chain Monte Carlo (MCMC) methods have been proposed in extreme value analysis (EVA) for assessing the flood risk in a certain location. The Hamiltonian Monte Carlo (HMC) method was employed to obtain the approximations to the posterior marginal distribution of the Generalized Extreme Value (GEV) model by using annual maximum discharges in two major river basins in Bangladesh. The discharge records of the two largest branches of the Ganges-Brahmaputra-Meghna river system in Bangladesh for the past 42 years were analysed. To estimate flood risk, a return level with 95% confidence intervals (CI) has also been calculated. Results show that, the shape parameter of each station was greater than zero, which shows that heavy-tailed Frechet cases. One station, Bahadurabad, at Brahmaputra river basin estimated 141,387 m3s-1 with a 95% CI range of [112,636, 170,138] for 100-year return level and the 1000-year return level was 195,018 m3s-1 with a 95% CI of [122493, 267544]. The other station, Hardinge Bridge, at Ganges basin estimated 124,134 m3 s-1 with a 95% CI of [108,726, 139,543] for 100-year return level and the 1000-year return level was 170,537 m3s-1 with a 95% CI of [133,784, 207,289]. As Bangladesh is a flood prone country, the approach of Bayesian with HMC in EVA can help policy-makers to plan initiatives that could result in preventing damage to both lives and assets.