In this manuscript, we apply a new technique named the Laplace Decomposition Method (LDM) to the fractional differential equation called the Riccati equation. Laplace Decomposition Method (LDM) is based on the Laplace Transform Method (LTM) and Adomain Decomposition Method (ADM). We attempt to give an estimated solution to the fractional Riccati differential equation using Laplace decomposition method and we also observe the behavior of the solution obtained. LDM makes it very easy to solve linear and non-linear fractional differential equations and gives exact solutions in the form of convergence series. The graphical interpretation of the behavior of the result is also given at the end of this manuscript, which is comparable with the results obtained by other methods.