The quantum system with H+2 impurity in two-dimensional square quantum dots is solved by using finite difference method, and discrete Schrdinger equation is obtained. The energy of electrons in ground state in the system and binding energy of impurity are calculated numerically. Effects of impurity ions with different spacing on the ground state energy and binding energy of electrons in different sizes of quantum dots are discussed. Calculation results show that the electron ground state energy in quantum dots is a function of the impurity position and quantum dot size. The ground state energy decreases rapidly and then increases slowly with increasing of quantum dot size, and it tends to a fixed value finally. The binding energy of impurity to electron decreases with increasing of quantum dot size. The smaller the impurity spacing is, the greater the influence of the quantum dot ground state energy will be.