Double two-body model is the fundamental conception model for solving Earth-Moon transfer orbit. The traditional approaches use the latitude and longitude of entry point on the sphere of influence to describe double two-body model, while in this paper a geometrical representation method of double two-body model by using parameters in orbital plane of flight trajectory was proposed. The search space on three-dimensional sphere was reduced to be a two-dimensional circle formed by tangent of the orbital plane and the sphere of influence, the shape parameter of Earth-Moon transfer orbit can be efficiently solved by one-parameter Brent root-finding algorithm and Lambert theory. In order to avoid double calculation, the orbital multivariate search problem calculated by the transfer orbit window was decoupled into two sub-problems, the transfer orbit shape parameter solution problem and the transfer orbital plane space orientation problem, which reduce the solution dimension of the problem, The two-stage method with parallel computing was approached in order to make full use of the nowadays computational power of multi-core computer. The simulation results show that the new parallel double two-body model with the use of geometrical section of orbital plane can be successfully applied to the analysis of the Earth-Moon transfer orbit from space elevator.