Full-waveform inversion is a promising tool to produce accurate and high-resolution subsurface models. Conventional full-waveform inversion requires an accurate estimation of the source wavelet, and its computational cost is high. We develop a novel source-independent full-waveform inversion method using a hybrid time- and frequency-domain scheme to avoid the requirement of source wavelet estimation and to reduce the computational cost. We employ an amplitude-semblance objective function to not only effectively remove the source wavelet effect on full-waveform inversion, but also to eliminate the impact of the inconsistency of source wavelets among different shots gathers on full-waveform inversion. To reduce the high computational cost of full-waveform inversion in the time domain, we implement our new algorithm using a hybrid time- and frequency-domain approach. The forward and backward wave propagation operations are conducted in the time domain, while the frequency-domain wavefields are obtained during modeling using the discrete-time Fourier transform. The inversion process is conducted in the frequency domain for selected frequencies. We verify our method using synthetic seismic data for the Marmousi model. The results demonstrate that our novel source-independent full-waveform inversion produces accurate velocity models even if the source signature is incorrect. In addition, our method can significantly reduce the computational time using the hybrid time- and frequency-domain approach compared to the conventional full-waveform inversion in the time domain.