Fifteen (15) fish species were collected from three (3) locations of the Brahmaputra River to determine heavy metals content in fish flesh, and to assess potential human health risk through consumption of those fishes. The contents of heavy metals in aqueous extract of different fish species were determined by an atomic absorption spectrophotometer (AAS) at the Department of Agricultural Chemistry, Bangladesh Agricultural University, during the period from March to June, 2018. The concentrations of Mn, Zn, Cu, Pb, Cd and Cr in different fish species ranged from 41.70-376.62, 38.98-279.08, 3.19-47.91, 2.20-3.73, 0.19-1.20 and 0.59-2.40 mg kg-1, respectively. The study results revealed that the edible portion of fish species of the river contained reasonably higher amount of Mn, Zn, Pb, Cr and Cu compared to some other previous studies carried out elsewhere with freshwater fishes. Among the fish species, mola (Amblypharyngodon mola) showed the highest metal pollution index (20.12) followed by chela (Salmophasia bacaila) (17.72), chanda (Chanda nama) (16.78) and chingri (Macrobrachium sp.) (15.83), while baim (Macrognathus aculeatus) exhibited the lowest (6.79). The calculated daily metal intake for Pb, Mn and Cd for both male and female were higher than that of upper tolerable intake level, which indicates consumption of common fishes of this river, is not safe. Similarly, target hazard quotient (THQ) values for Mn surpassed 5.0 for both male and female, and the same value for Pb also surpassed 5.0 for female indicate that the exposed population are unsafe. The study results also revealed that all individual THQ values of other metals for both male and female surpassed 1, which means exposed population are in level of concern interval. In Bangladesh freshwater river fishes are more popular than farm fishes. However, the study results recommend to aware people about heavy metal contents before consuming fish species of a polluted river system.