The Virtual Element Method (VEM) is a numerical technique that can be viewed as an extended form of the Finite Element Method. In the prior studies of the VEM, a stabilization term is required in order to ensure that the global stiffness matrix has the correct rank. In this work, we present a stabilization-free Virtual Element Method for compressible hyper-elastic materials in 2D. The main idea of the stabilization-free approach is to use an enhanced approximation space to compute a higher-order polynomial L_2 projection of the gradient. The first- and second-order polynomials are adopted and higher order format is discussed at the same time. Besides, the formulation of the stabilization-free VEM for hyper-elastic materials is given. Some numerical examples are given to compare the accuracy of the stabilization-free VEM with the conventional VEM.