This paper is concerned with a stability criterion of nonlinear feedback systems, called the shifted Popov criterion. It includes the Popov and circle criteria as special cases, and enables us to check stability in the frequency domain in a graphical manner. This paper derives an LMI representation of the shifted Popov criterion, both in the Lyapunov stability context and the input-output stability context, when the linear part of the nonlinear feedback system has a state-space realization.