In this paper we have studied Kaluza-Klein string cosmological model within the framework of f (R, T ) theory of gravity, where R is the Ricci scalar and T is the trace of the stress energy momentum tensor. We have obtained the solution of the corresponding field equations by using a time varying deceleration parameter. We also discussed various physical and dynamical properties of the model. The variation of different cosmological parameters are shown graphically for specific values of the parameters of the model.