Exact derivation method of all periodic solutions for zero stiffness, viscous damping free forced vibro-impact systems is proposed in this paper. First, specific initial condition which make solution periodize is determined using pseudo-feedback approach. By means of substitution this initial value into a globalized general solution, global function form of all periodic solutions includes symmetric and asymmetric types can be represented by superposition of periodic stationary solution of base linear system, finite number of weighted summation of periodic functions caused by impact nonlinearity and their constants parts. Two types of invariant relations for quantity of periodic solution are also derived. Finally, numerical simulation calculating typical asymmetric periodic solution is perfomed. The validity of the proposed method is confirmed.