The Virgo cluster is the nearest massive galaxy cluster and thus a prime target to study astrophysical processes in dense large-scale environments. In the radio band, we can probe the non-thermal components of the inter-stellar medium (ISM), intracluster medium (ICM) and of active galactic nuclei (AGN). With the ViCTORIA (Virgo Cluster multi-Telescope Observations in Radio of Interacting galaxies and AGN) project, we are carrying out multiple wide-field surveys of the Virgo cluster at different frequencies. We aim to investigate the impact of the environment on the evolution of galaxies and the contribution of AGN to the ICM-heating, from the inner cluster regions out to beyond the virial radius. We present a survey of the cluster at 120-168 MHz using LOFAR. We image a 132 deg2 region of the cluster, reaching an order of magnitude greater sensitivity than existing wide-field radio surveys of this field at three times higher spatial resolution compared to other low-frequency observations. We developed a tailored data processing strategy to subtract the bright central radio galaxy M87 from the data. This allowed us to correct for the systematic effects due to ionospheric variation as a function of time and direction. In the final mosaic with a resolution of 9"x5", we reach a median noise level of 140 μJy/beam inside the virial radius and 280 μJy/beam for the full area. We detect 112 Virgo member galaxies and 114 background galaxies. In at least 18 cases, the radio morphology of the cluster member galaxies shows clear signs of ram-pressure stripping. This includes three previously unreported candidates. In addition, we reveal for the first time 150 kpc long tails from a previous epoch of AGN activity for NGC 4472 (M 49). While no cluster-scale diffuse radio sources are discovered, we find the presence of an extended radio signature of the W′-group.