Under uncontrolled conditions, voltage-controlled suspension-type magnetic levitation systems are unstable systems in which a levitated object either falls or is attracted to the electromagnet. Furthermore, the magnetic force and the electrical characteristics of the circuit have strong nonlinearities. This study applies fractional-order linear quadratic regulator (LQR) control, which combines fractional calculus and modern control theory, to a benchmark problem: a voltage-controlled suspension-type magnetic levitation system. Furthermore, a fractional-order servo LQR control method is developed for a case in which a levitated object is controlled to a target position that deviates from the equilibrium point. To perform state-feedback control such as fractional-order servo LQR control, which requires information of all the states, a fractional-order state-observer is designed to estimate fractional-order states. Simulation results demonstrate that fractional-order servo LQR control enables us not only to achieve stabilization of the equilibrium point; it also enables target-value tracking. Experimental results confirmed that the fractional-order servo LQR control provides higher control performance than that of conventional integer-order servo LQR control.