In this paper, we consider a new kind of
Fletcher-Reeves (abbr. FR) conjugate gradient method with
errors, which is broadly applied in neural network training. Its
iterate formula is $x_{k+1}=x_{k}+\alpha_{k}(s_{k}+\omega_{k})$,
where the main direction $s_{k}$ is obtained by FR conjugate
gradient method and $\omega_{k}$ is accumulative error. The global
convergence property of the method is proved under the mild
assumption conditions.