A three-body model proposed earlier (S. Kumar and V. S. Bhasin, Phys. Rev.C65, 034007 (2002)) to set up the wave function of 11 Li is extended to investigate structural properties of 11 Li like matter radius, momentum distributions of the halo neutrons and the core(c), and n–n and n–c correlations. The energies and widths of experimentally observed resonant states of 11 Li in continuum have been calculated by employing the complex scaling method. The model is further extended to study the β-decay of 11 Li to the decay modes: (i) deuteron + 9 Li channel and (ii) 11 Be * (18.3 MeV) state. The results obtained are found to be in reasonably good agreement with the experimental data.