Abstract: Based on the moving least-square (MLS) approximation, the moving least-square approximation with complex variables (MLSCV) is presented in this paper. And the moving least-square approximation with complex variables based on the orthogonal basis function is discussed in detail. The method can not form an ill-conditioned system of equations. The meshless method obtained from the moving least-square approximation with complex variables has greater computational efficiency. Then, combining the moving least-square approximation with complex variables and the boundary element-free method (BEFM) for elasticity, the boundary element-free method with complex variables (BEFMCV) for elasticity is presented, and the corresponding formulae are obtained. The boundary element-free method with complex variables is a direct numerical method of the meshless method of boundary integral equation. And the boundary condition can be applied easily. The boundary element-free method with complex variables has a greater precision. Some numerical examples are given at last.