A grid-free compressive sensing (CS) based method for extracting the normal modes of acoustic propagation in the ocean waveguide from vertical line array (VLA) data is presented. Extracting the normal modes involves the estimation of mode horizontal wavenumbers and the corresponding mode shapes. Sparse representation of the waveguide propagation using modes at discrete horizontal wavenumbers enables CS to be applied. Grid-free CS, based on group total-variation norm minimization, is adopted to mitigate the issues of the wavenumber search grid discretization in the conventional CS. In addition, the suggested method can process multiple sensor data jointly, which improves performance in estimation over single sensor data processing. The method here uses data on a VLA from a source at several ranges, and processes the multiple sensor data at different depths jointly. The grid-free CS extracts the mode wavenumbers and shapes even with no a priori environmental knowledge, a partial water column spanning array data, and without the mode orthogonality condition. The approach is illustrated by numerical simulations and experimental SWellEx-96 (shallow water evaluation cell experiment 1996) data.