In this paper, we investigate a fractional-order predator-prey model incorporating prey harvesting. In a non-delayed model, the functional response of Crowley-Martin has been studied. We first prove the existence, uniqueness, non-negativity, and boundedness of the solutions for the proposed model. Furthermore, analyze the existence of various equilibrium points to examine the locally asymptotically stable properties, and use the suitable Lyapunov function to study the globally asymptotic stability. Finally, some numerical simulations are verified for the analytical results.