In this paper, a general FRW cosmological model has been constructed in f(R,T) gravity reconstruction with variable cosmological constant. A number of solutions to the field equations has been generated by utilizing a form for the Hubble parameter that leads to Berman's law of constant deceleration parameter q = m-1. The possible decelerating and accelerating solutions have been investigated. For(q > 0) we get a stable flat decelerating radiation-dominated universe at q = 1. For(q < 0) we get a stable accelerating solution describing a flat universe with positive energy density and negative cosmological constant. Nonconventional mechanisms that are expected to address the late-time acceleration with negative cosmological constant have been discussed.
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