Concentrations of natural and fall-out radionuclides in the offshore seawater and sediment from some parts of the Bay of Bengal, Bangladesh, were determined using a coaxial germanium detector. The average activities of U-238, Th-232, K-40 and Cs-137 were recorded as 31.2 +/- 5.8, 51.9 +/- 9.4, 686.4 +/- 170.5 and 0.5 +/- 0.6 Bq kg(-1) dry weight, respectively, for sediment, and 4.8 +/- 1.2, 5.4 +/- 1.2 and 39.1 +/- 8.6 Bq L-1 for U-238, Th-232 and K-40, respectively, in seawater. The concentration of Cs-137 in seawater was below the detection limit. The concentration of sediment U-238 was found to be positively correlated with Th-232 (, p<0.05) and K-40 (r=0.96, p<0.01), while Th-232 was positively correlated with K-40 (r=0.91, p<0.05). In sediment, the concentration of U-238 was negatively correlated (r=-0.86, p<0.05) with sea depth. In the seawater sample, the only significant relationship found was between concentration of Th-232 and water depth (r=-0.86, p<0.05). One-factor analysis of variance (ANOVA) showed that the level of radioisotope concentrations of seawater and sediment was highly significant for U-238 (F=122, df=11, p=0.01), Th-232 (F=143, df=11, p=0.01) and K-40 (F=86, df=11, p=0.01). The results showed that the level of radioactivity decreased from coast to open sea. Imminent threat due to radioactivity was not observed in these parts of the Bay of Bengal.