Based on the modified FR type spectral conjugate gradient method, the conjugate parameters and spectral coefficients are improved, and hence a sufficiently descending spectral conjugate gradient method is proposed. The spectral conjugate gradient method's global convergence is established under the standard Wolfe line search criteria. Finally, numerical experiments are carried out to compare the proposed method with two FR spectral conjugate gradient methods proposed in other literatures. The numerical results indicate that the proposed method enjoys certain advantages in numerical calculation.