A new approach for the classification of the cosmic web is presented. In extension of the previous work of Hahn et al. and Forero-Romero et al., the new algorithm is based on the analysis of the velocity shear tensor rather than the gravitational tidal tensor. The procedure consists of the construction of the shear tensor at each (grid) point in space and the evaluation of its three eigenvectors. A given point is classified to be either a void, sheet, filament or a knot according to the number of eigenvalues above a certain threshold, 0, 1, 2 or 3, respectively. The threshold is treated as a free parameter that defines the web. The algorithm has been applied to a dark matter only simulation of a box of side length 64 h−1 Mpc and N = 10243 particles within the framework of the 5-year Wilkinson and Microwave Anisotropy Probe/Λ cold dark matter (ΛCDM) model. The resulting velocity-based cosmic web resolves structures down to ≲0.1 h−1 Mpc scales, as opposed to the ≈1 h−1 Mpc scale of the tidal-based web. The underdense regions are made of extended voids bisected by planar sheets, whose density is also below the mean. The overdense regions are vastly dominated by the linear filaments and knots. The resolution achieved by the velocity-based cosmic web provides a platform for studying the formation of haloes and galaxies within the framework of the cosmic web.