In this paper, conformal symmetric Freidmann-Robertson-Walker (FRW) universe with perfect fluid in the framework of f(R, T) gravitational theory is investigated. Firstly, field equations of FRW universe with perfect fluid are obtained for f (R, T) = R + h(T) modified theory of gravity. The field equations of the model have been revised to understand physical nature between matter and geometry by means of conformal symmetry in f(R, T) gravitational theory. The exact solutions of conformal FRW universe with perfect fluid are attained for matter part of the f(R, T) model in the case of h(T) = lambda T. The f (R, T) gravitational theory is one of the acceptable modifications of General Relativity (GR) in order to expound cosmic acceleration of the universe with no needing any exotic component. Nevertheless, the obtained model indicates exotic matter distribution for the current selection of arbitrary constants. Also, different value selections of arbitrary constants for the obtained model are able to predicate expanding or contracting universe with zero deceleration. Besides, it is shown that the FRW universe under the influence of the conformal Killing vector preserves to isotropic nature. Energy conditions are investigated. Also, it is shown that the constructed model satisfies strong energy condition (SEC) in all cases.