Usually, conjugate gradient methods depend on choices of a descent search direction. In addition, some conjugate gradient methods also depend on line searches. In this paper, the authors propose a general form of three-term conjugate gradient methods which always satisfy a sufficient descent condition, independently of the choice of some parameter and line searches. This general form includes search directions including some modified FR methods. The present paper is organized as follows. In Section 2, the authors construct a general form of three-term conjugate gradient methods which satisfy sufficient descent condition and give a sufficient condition for its global convergence. In Section 3, they propose a specific three-term conjugate gradient method based on the multistep quasi-Newton method, and they prove its global convergence by using the result from Section 2. Finally, in Section 4, some numerical experiments are presented.