Band structures near yrast lines of the Z = N doubly magic nucleus 56Ni are investigated with the configurationdependent cranked Nilsson-Strutinsky approach. The observed deformed bands are confirmed as highly deformed and their properties are explained theoretically. The calculated transition quadrupole moments Qt, ～ 1.7 eb at low spin as well as the kinematic and dynamic moments of inertia J1) and J(2) for configurations of interest are found to be generally in good agreement with the observed results. Two terminating states at 20+ and 29- for the two observed bands and other terminations in 56Ni are also predicted. It is found that the configuration-dependent cranked Nilsson-Strutinsky approach is better in the description of nuclear properties and band structures at high spin than other models.