A phenomenological potential model, the modified flat-bottom potential, is assumed according to the flat-bottom potential and some physical considerations for the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling. Then, the propagator functions and mass function for the quark, and the Bethe-Salpeter wave functions, mass, electromagnetic form factor, radius and decay constant for the pion are calculated numerically in the framework of the Schwinger-Dyson and Bethe-Salpeter equations with the modified flat-bottom potential. In order to obtain these, the Schwinger-Dyson and Bethe-Salpeter equations in the modified flat-bottom potential model are solved simultaneously by numerical iteration in the ladder approximation, and without any further one. Our results for the asymptotic quark mass function and the bound state wave functions agree with those derived from other theories and for the electromagnetic form factor, mass, radius and decay constant of the pion agree with experimental results, respectively. (author). 14 refs, 9 figs.