Mixing of two stratified miscible fluids in an eccentric stirred tank agitated by a four pitched-blade turbine was studied by using the detached eddy simulation (DES) model and volume of fluid(VOF) method. The fluids were operated in the transitional and mildly turbulent flow regimes. Interfaces between the two miscible fluids during the mixing processes were captured and mixing times were computed. Effects of the Richardson number and eccentricity on the mixing times were quantificationally analyzed. Results show that the spatial and temporal variations of volume fractions of the fluids can be well captured by the method presented in this study. Mixing time increases with the increase of Richardson number. Effect of eccentricity on mixing time depends on Richardson number and the eccentric agitation scheme is not advisable to use to blend the low-viscosity miscible fluids starting from a stratified state, especially for lower Richardson values.