The complex optical conductivity of the half-Heusler compound GdPtBi is measured in a frequency range from 20 to 22 000 cm^{-1} (2.5 meV-2.73 eV) at temperatures down to 10 K in zero magnetic field. We find the real part of the conductivity, σ_{1}(ω), to be almost perfectly linear in frequency over a broad range from 50 to 800 cm^{-1} (∼6-100 meV) for T≤50 K. This linearity strongly suggests the presence of three-dimensional linear electronic bands with band crossings (nodes) near the chemical potential. Band-structure calculations show the presence of triple points, where one doubly degenerate and one nondegenerate band cross each other in close vicinity of the chemical potential. From a comparison of our data with the optical conductivity computed from the band structure, we conclude that the observed nearly linear σ_{1}(ω) originates as a cumulative effect from all the transitions near the triple points.