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Geometric approximation errors of periodically distributed surface facets of cable-network reflector antennas can result in grating lobes undesired in some space missions. As the surface is shaped by the tensioned flexible cable-network structure, the electromagnetic (EM) and structural parameters are highly correlated, and the well-designed surface obtained only concerning the EM performance may not be shaped by the tension-only cable network with specified cable-tension constraints. To address the problem, this study proposes an integrated structural-EM optimization method to enable low grating lobe cable-network antenna design. In this method, force densities of the cables, which can determine both the cable tensions and surface node positions that decide the boundary conditions of the EM field, are selected as the design variables. An adaptive objective/constraint function is proposed, which enables the grating lobe level (GLL) to be minimized with constrained cable tensions, antenna gain, and first sidelobe level (SLL) in a simultaneous, feasible and relatively fast way. To demonstrate the feasibility and effectiveness of the proposed method, it was implemented on a 12 m-diameter cable-network antenna. The results indicate that the grating lobes are greatly degraded and the achieved surface can be formed by well tensioned cables. [ABSTRACT FROM AUTHOR]