In this communication, we report direct and unambiguous evidence of the existence of inner semiconducting tube photoluminescence (PL) from measurements performed on four individual freestanding index-identified double-walled carbon nanotubes (DWNTs). Based on thorough Rayleigh scattering, Raman scattering, and PL experiments, we are able to demonstrate that the inner semiconducting tube PL is observed with a quantum yield estimated to be a few 10-6 independent of the semiconducting or metallic nature of the outer tube. This result is mainly attributed to ultrafast exciton transfer from the inner to outer tube. Furthermore, by carrying out PL excitation experiments on the (14,1)@(15,12) DWNT, we show that the inner semiconducting tube PL can be detected through the optical excitation of the outer tube, indicating that the exciton transfer can also occur in the opposite way.