Composite materials exhibit diverse microstructure distributions, with periodic microstructures being a typical pattern. Periodic structures feature repeating basic cells, representing the situation where the inclusion arrangement within a material changes from completely disordered to strictly ordered. Modern composite material design, especially computer-aided material design, usually refers to the design of periodically distributed cells. Multi-coating refers to a new type of coating in which the geometric parameters are proportional on the thickness coordinate. Multi-coating can achieve gradient changes in material parameters, allowing for gradient changes in the mechanical properties of the coating and thereby enabling the design and control of material properties such as strength, toughness, and stiffness. Nanocomposites possess unique mechanical properties. When the structural size of the reinforcing phase reaches the nanoscale, the surface effect cannot be ignored. The macroscopic mechanical properties of nanocomposites are different from those of traditional composites. In this work, based on the unit cell method of micromechanics and the Gurtin-Murdoch theory of surface elasticity, the elastic field and effective property of periodic coated-fiber nanocomposites subjected to longitudinal shear loads are studied. The analytical solution for the longitudinal shear effective modulus of periodic nanocoated composites is obtained using the unit cell functional variational method and the eigenfunction expansion method. The consistency between the obtained solution and the existing results indicates the validity of the proposed method. The macroscopic effective property of periodic nanocomposites can be controlled by changing the microstructure parameters of the multi-coating. The effects of coating mechanical properties, coating geometric parameters, surface properties and fiber volume fraction on the effective properties of the composite are discussed. The analytical method proposed in this paper and the obtained results provide a theoretical basis for the design of periodic nanocoated fiber composites and the regulation of their mechanical properties.