In general, seismic waveform inversion adopts an objective function based on the l₂-norm. However, waveform inversion using the l₂-norm produces distorted results because the l₂-norm is sensitive to statistically invalid data such as outliers. As an alternative, there have been several studies applying l₁-norm-based objective functions to waveform inversion. Although waveform inversion based on the l₁-norm is known to produce robust inversion results against specific outliers in the time domain, its effectiveness and characteristics are yet to be studied in the frequency domain. The present study proposes an algorithm for l₁-norm-based waveform inversion in the frequency domain. The proposed algorithm employs a structure identical to those used in conventional frequency-domain waveform inversion algorithms that exploit the back-propagation technique, but displays robustness against outliers, which has been confirmed based on inversion of the synthetic Marmousi model. The characteristics and advantages of the l₁-norm were analysed by comparing it with the l₂-norm. In addition, inversion was performed on data containing outliers to examine the robustness against outliers. The effectiveness of removing outliers was verified by using the l₁-norm to calculate the residual wavefield and its spectrum for the data containing outliers.