We investigate the linear optical conductivities of the newly-discovered triple-component semimetals. Due to the exactly flat band, the optical conductivity relates to the transition between the zero band and the conduction band directly reflecting the band structure of the conduction electrons in contrast to the other materials. For the low-energy models with various monopole charges, the diagonal conductivities show strong anisotropy. The ω-dependence of interband conductivities for a general low-energy model is deduced. The real part of the interband σ_xx always linearly depends on the optical frequency, while the one of σ_zz is proportional to ω^{2/n-1}. This can be a unique fingerprint of the monopole charge. For the lattice models, there also exists the optical anomalous Hall conductivity, where a sign change may appear. The characteristic frequencies of the kink structures are calculated, strictly. Our work will help us to establish the basic picture of linear optical response in topological triple-component semimetals and identify them from other materials.