Our previous research found that CFRPs fabricated by the electrodeposition resin molding (ERM) method exhibited high damping properties. In this research, tailored fiber placement (TFP) was used to make curved fiber shapes, however, those shapes were limited to a parabola and a sine curve. Linear combination of radial basis functions (RBFs) were used to make more complex fiber shapes, and optimum fiber shapes are investigated to improve damping of CFRPs fabricated by the ERM method. Damping is modeled by the specific damping capacity (SDC) which is defined as the ratio of dissipated energy and maximum strain energy, and total damping properties of CFRPs are calculated using finite element analysis (FEA). Before optimization, material SDCs of a plain weave sheet and a TFP layer, which are compositions of CFRPs, are identified by particle swarm optimization (PSO) using the results of experimental modal analysis and FEA. Then, fiber shapes were optimized to maximize the first modal SDC of L-shaped and T-shaped plates using PSO with nonlinear dissipative term. Simultaneously, the thickness distribution which is caused by overlaps or gaps between curved fibers was estimated and applied to a finite element model for more accurate numerical estimation. The results showed that the present optimization of curved fiber shapes including estimation of thickness distribution improves the first modal SDC and decreases the volume of a TFP layer in comparison with unidirectional fiber shapes.