Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to L_p-version of the Petty's conjectured projection inequality is developed by using the notions of the L_p-mixed volume and the L_p-dual mixed volume, the relation of the L_p-projection body and the geometric body T_-pK, the Bourgain-Milman inequality and the L_p-Busemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body T_-pK, the reverses of L_p-version of the Petty's conjectured projection inequality and the L_p-Petty projection inequality are given, respectively.