The Bethe-Salpeter equation for bound states of a spinor straton-antistraton pair is discussed under the assumption that the interaction between the straton-antistraton pair is purely scalar and may be described by a relativistically covariant v-potential. The structure wave function of the meson is expanded according to the O(4) group, and solved numerically first by keeping the lowest partial waves, and then the in-fluence of the higher partial waves are considered. Numerical results of the wave functions are given both in the momentum space and configuration space, and the mean square radius of the meson is evaluated. It is shown that the low partial wave-large component approximation is valid for tightly bound systems. As a comparison, the loosely bound systems are also discussed.