We present comprehensive and elaborate study of W LVI (K-likeW55+) by using multi-configuration Dirac-Fock method (MCDF). We have included relativistic corrections, QED (Quantum electrodynamics) and Breit corrections in our computation. We have reported energy levels and radiative data for multipole transitions i.e. electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1) and magnetic quadrupole (M2) within lowest 142 fine structure levels and predicted soft x-ray transition (SXR) and extreme ultraviolet transitions (EUV) from higher excited states to ground state. We have compared our calculated data with energy levels compiled by NIST and other available results in literature and small discrepancies found with them are discussed. Since only few lowest levels are only available in the literature, therefore for checking excitation energies of higher excited states, we have performed same calculations with distorted wave method. Furthermore, we have also provided relative population for first five excited states, partition function and thermodynamic quantities for both W LVI and studied their variations with temperature. We believe that our reported new atomic data of W LVI may be useful in identification and analysis of spectral lines from various astrophysical and fusion plasma sources and also beneficial in plasma modeling.