This is the study of the grade-III fluid having the unidirectional and unsteady flow. Differential equation is solved using perturbation method to get linear forms of the velocities. The velocity u(y,t) is perturbed in ε to get the two-linear Partial Differential Equations (PDE's) in terms of u₀(y,t) and u₁(y,t). The solution of 1^st linear is given in the exponent form f(y) e^iat , that gives an ordinary differential equation that is easily solved to get the solution. This solution u₀(y,t) is then utilized in Partial Differential Equation of 1^st term velocity u₁(y,t) and that gives linear Partial Differential Equation in the velocity u₁(y,t). The solution of u₁(y,t) is given in the exponent form F(y) e^3iat , that gives an ordinary differential equation in F(y), that is solved to get the solution of F(y). This gives the perturbed solution for u₁(y,t) in the form of F(y). First and zeroth solutions for the velocities give the solution for PDE.