In this study, the solutions of the random component time-fractional Klein-Gordon equation is obtained as approximately or exactly. The initial condition of this Klein-Gordon equation is studied by Gamma distribution. The fractional derivatives are defined in the Caputo sense. An example is shown to illustrate the influence of the solutions obtained by the new Sumudu transform iterative method (NSTIM). The expected value and variance of these solutions of this Klein-Gordon equation are obtained. The approximate analytical solution of this equation obtained by NSTIM and VIM are compared. NSTIM is applied to analyze the solution of this equation. Solution and figures are obtained by using MAPLE software. The formulas for the expected values and variances and results from the simulations of this Klein-Gordon equation are compared and the efficiency of this method is investigated.