Studying the system of a spin-1/2 particle and a spin-1/2 anti-particle with combinations of the Fermitype interactions (including the spin-spin interaction) and methods to deal with divergent integrals, we obtain two J^P = O^- bound-state solutions and examine electromagnetic form factors of them. Main results are the following: (I) One of the obtained solutions is a positronium-like bound state. It is obtained by taking the cut-off momentum K to be finite, and the em form factor of it has striking features due to K. The cutting off the momentum is found to be unfacourable for understanding available experimental data on the pion em form factor. (II) The other of the obtained solutions is found to be a Nambu-Goldstone boson. It is able to be obtained by taking K of K→∞ and performing a renormalization operation by virtue of a form factor in the basic equation. The em form factor of it is consistent with experimental data at large Q^2's. This bound-state solution is very interesting.