Abstract The solar wind in the inner heliosphere has been observed by Parker Solar Probe (PSP) to exhibit abundant wave activities. The cyclotron wave modes responding to ions or electrons are among the most crucial wave components. However, their origin and evolution in the inner heliosphere close to the Sun remains a mystery. Specifically, it remains unknown whether it is an emitted signal from the solar atmosphere or an eigenmode growing locally in the heliosphere due to plasma instability. To address and resolve this controversy, we must investigate the key quantity of the energy change rate of the wave mode. We develop a new technique to measure the energy change rate of plasma waves, and apply this technique to the wave electromagnetic fields measured by PSP. We provide the wave Poynting flux in the solar wind frame, identify the wave nature to be the outward propagating fast-magnetosonic/whistler wave mode instead of the sunward propagating waves. We provide the first evidence for growth of the fast-magnetosonic/whistler wave mode in the inner heliosphere based on the derived spectra of the real and imaginary parts of the wave frequencies. The energy change rate rises and stays at a positive level in the same wavenumber range as the bumps of the electromagnetic field power spectral densities, clearly manifesting that the observed fast-magnetosonic/whistler waves are locally growing to a large amplitude.