This paper presents a design study for a field-cycled magnetic resonance imaging (MRI) system directed at small animal imaging applications. A field-cycled MRI system is different from a conventional MRI system in that it uses two separate and dynamically controllable magnetic fields. A strong magnetic field is used to polarize the object, and a relatively weak magnetic field is used during signal acquisition. The potential benefits of field-cycled MRI are described. The theoretical dependences of field-cycled MRI performance on system design are introduced and investigated. Electromagnetic, mechanical and thermal performances of the system were considered in this design study. A system design for imaging 10 cm diameter objects is presented as an example, capable of producing high-duty-cycle polarizing magnetic fields of 0.5 T and readout magnetic fields corresponding to a proton Larmor frequency of 5 MHz. The specifications of the final design are presented along with its expected electromagnetic and thermal performance.