The radiative lifetime of exciton, trions and biexciton in CdSe/CdS core–shell quantum dot has been calculated using effective mass approximation. The eigen-value and eigen-functions were obtained by solving Schroedinger and Poisson equations in a self-consistent iterative manner. The observed ratio of lifetimes of exciton and biexciton τ(x):τ(xx) is 2:1. The trions have a radiative lifetime similar to that of a monoexciton. Variation of radiative lifetimes with core radius and shell thickness was studied. Our investigations of Stark effect on this system point that only in the weak confinement region the external electric field has a control on the radiative lifetime.