||In this paper, the fractional-order complex T system is proposed. The dynamics of the system including symmetry, the stability of equilibrium points, bifurcations with variation of system parameters, and derivative orders are investigated. Period-doubling and tangent bifurcations with appropriate derivative orders and system parameters are observed. Besides, the control problem of the system is examined by using the feedback control technique. Furthermore, based on the stability theory of fractional-order systems, the scheme of function projective synchronization for the fractional-order complex T system is presented. The function projective synchronization for the system is realized by designing an appropriate synchronization controller. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.