This chapter studies the numerical solution of Phase-Lag quadratic integral equations (P-LQIE). Using Taylor expansion in fractional form reduces the P-LQIE to fractional quadratic integral equations. Then, using shifted Chebyshev polynomials of the eighth kind (SCP8K), we obtain a system of nonlinear algebraic equations (NAS). Banach fixed point theorem is applied to demonstrate the existence and uniqueness of the solution to P-LQIE. Also, the convergence and stability of the solution are discussed. Finally, some numerical applications are suggested to describe the theoretical results. All the computations are obtained by Maple 18 software.