In the gravitational theory based on Lyra's geometry, we study the Friedmann Robertson Walker (FRW) cosmological model in the presence of perfect fluid. Exact solutions of the Einstein equations are obtained and discussed in the following cases: (i) β(t) ( the time component of the displacement vector introduced by Lyra ) is a constant, (ii) β(t) is time-dependent and q (the deceleration parameter of the model ) is a constant and (iii) β(t) and q are functions of time t. The Thermodynamic functions of the universe are calculated and studied for the case k=0,1,-1 flat, open, and closed universe respectively. The entropy of the universe is obtained as a constant which means we deal with a stage of evolution in which the universe is adiabatic. The distance modulus for our model is calculated at different values of the red shift and compared with the results obtained in supernovae la. The physical and geometrical properties of the obtained models are discussed.