A recently developed helicity basis for nucleon-nucleon (NN) scattering is applied to the deuteron bound state. Here the total spin of the deuteron is treated in such a helicity representation. For the bound state, two sets of two coupled eigenvalue equations are developed, where the amplitudes depend on two variables and one variable, respectively. Numerical illustrations based on the realistic Bonn-B NN potential are given. In addition, an "operator form" of the deuteron wave function is presented, and several momentum dependent spin densities are derived and shown, in which the angular dependence is given analytically.