To solve large-scale unconstrained optimization problems, this paper further investigated the RMIL conjugate gradient method and its variants in order to propose two new spectral conjugate gradient methods. Under basic assumptions for unconstrained optimization problems, where the level set was bounded and the gradient was Lipschitz continuous, the search directions generated by the proposed methods satisfied the sufficient descent property independent of the choice of line search. Moreover, the global convergence of the methods was established under both the standard Wolfe line search and the standard Armijo line search. Numerical experiments on unconstrained optimization and image denoising problems under both line searches demonstrated that the two proposed spectral conjugate gradient methods exhibited superior performance and broader applicability.