In conventional full-waveform inversion (FWI), viscous effects are typically neglected, and this is likely to adversely affect the recovery of P-wave velocity. We have developed a strategy to mitigate viscous effects based on the use of matching filters with the aim of improving the performance of acoustic FWI. The approach requires an approximate estimate of the intrinsic attenuation model, and it is one to three times more expensive than conventional acoustic FWI. First, we perform 2D synthetic tests to study the impact of viscoacoustic effects on the recorded wavefield and analyze how that affects the recovered velocity models after acoustic FWI. Then, we apply the current method on the generated data and determine that it mitigates viscous effects successfully even in the presence of noise. We find that having an approximate estimate for intrinsic attenuation, even when these effects are strong, leads to improvements in resolution and a more accurate recovery of the P-wave velocity. Then, we implement and develop our method on a 2D field data set using Gabor transforms to obtain an approximate intrinsic attenuation model and inversion frequencies of up to 24 Hz. The analysis of the results indicates that there is an improvement in terms of resolution and continuity of the layers on the recovered P-wave velocity model, leading to an improved flattening of gathers and a closer match of the inverted velocity model with the migrated seismic data.