In this paper, we have proposed a new form for the varying deceleration parameter that is a generalization of the form of O. Akarsu and T. Dereli [Cosmological models with linearly varying deceleration parameter, Int. J. Theor. Phys. 51 (2012) 612]. LRS Bianchi type-I cosmological model filled with a perfect fluid source in f(R, T) gravity theory, where R is the Ricci scalar and T is the trace of the stress energy-momentum tensor, has been studied in order to investigate early time deceleration and late time acceleration of the universe by using this new form of time-varying deceleration parameter. The time evolution of physical and dynamical parameters have been analyzed and shown by graphs. Moreover, the deceleration parameter has been considered in terms of redshift. It has been shown that the model starts with a big bang and ends with a big rip. It is filled by a quintessence like fluid at the early time and by a phantom like fluid at the late time.