<p>For some ill-conditioned problems, the search direction generated by a nonlinear conjugate gradient (CG) method may be included in the subspace spanned by the previous search directions due to the propagation of rounding errors, and the iteration may fall into a local loop in this case. Based on a three term Hestenes–Stiefel (HS) nonlinear conjugate gradient method, a limited memory HS method is developed. When the current search direction is approximately included in the subspace spanned by the preceding directions stored in the memory, the process switches to optimize the objective function on the subspace by using limited memory BFGS method to avoid potential local loop. The algorithm turns back to the full space iteration at an approximate solution on the subspace. The proposed method is sufficient descent and the search direction is relative to both the quasi-Newton direction and the CG direction. We analyze the global convergence properties of the proposed algorithm under some mild conditions. Numerical experiment shows that the proposed method is efficient for the CUTEst test problems.</p>