A modified spectral conjugate gradient method is proposed to solve unconstrained optimization problems. The search direction of the algorithm is the descent direction, and it has global convergence under the Wolfe-Powell line search. It is proved that the algorithm has a linear convergence rate under some suitable conditions. Some numerical experiments on some standard functions show that the algorithm is effective on the facts including number of iteration, number of function calculations and program running time, and has certain advantages compared with related algorithms. Finally, the algorithm is applied to image denoising problems. Some different noise effects are applied for the classical images Lena and Camera. The comparison with related algorithms in references shows that the algorithm has good image denoising effect about the fact of the PSNR.