Intention tremor refers to the rhythmic and involuntary contraction and relaxation of muscles with movement towards a target, which is a common sequela of multiple sclerosis and usually occurs in the distal joints of the upper limb. Functional electrical stimulation (FES) is feasible for tremor suppression because of its fewer side effects, low-cost and portability. Most existing FES based design methods assume that tremor is a single frequency signal, though it is multi-frequency in reality. The idealized simplification will limit the performance of tremor suppression. To address the problem, this paper proposes an FES-based multi-periodic repetitive control scheme to suppress multiple frequency wrist tremor. Firstly, a nonlinear wrist musculoskeletal model with Hammerstein structure is established. Then, a control strategy combining the model inverse linearization control and multi-periodic repetitive control is proposed for tremor suppression. A frequency modified inverse repetitive control algorithm and a gradient-based repetitive control algorithm are developed to regulate the FES level. Finally, comparative experiments on four unimpaired participants and an intention tremor patient are conducted to validate the effectiveness of the proposed control schemes. Experimental results show that the multi-periodic repetitive control scheme can suppress tremor by up to 90.52%. Compared with the traditional filter based feedback controller and the single periodic repetitive controller, the proposed multi-periodic repetitive controller can achieve an average of 26% and 16% improvement respectively in tremor suppression, demonstrating the advantages of the proposed design.