This paper presents a comparison study on continuous and discrete optimal control of a gantry crane. Hence, the nonlinear dynamic model of the system is derived via Lagrange's principle, the linearized equations of the system is expressed. The motor voltage of and displacement of the trolley are presumed as input and output of the system respectively, and the state-space equations of the system are presented. Then, optimal continuous and discrete optimal feedback control law is obtained for tracking of trolley, and some tracking simulation are performed which compare the results of continuous and discrete optimal law.