This paper presents the experimental results on the Terapia Oncologica con Protoni-Intensity Modulated Proton Linear Accelerator (TOP-IMPLART) beam that is currently accelerated up to 35 MeV, with a final target of 150 MeV. The TOP-IMPLART project, funded by the Innovation Department of Regione Lazio (Italy), is led by Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA) in collaboration with the Italian Institute of Health and the Oncological Hospital Regina Elena-IFO. The accelerator, under construction and test at ENEA-Frascati laboratories, employs a commercial 425 MHz, 7 MeV injector followed by a sequence of 3 GHz accelerating modules consisting of side coupled drift tube linac (SCDTL) structures up to 71 MeV and coupled cavity linac structures for higher energies. The section from 7 to 35 MeV, consisting on four SCDTL modules, is powered by a single 10 MW klystron and has been successfully commissioned. This result demonstrates the feasibility of a "fully linear" proton therapy accelerator operating at a high frequency and paves the way to a new class of machines in the field of cancer treatment.