On the basis of recent experiment, the focusing and leading effect of an ultra-cold Bose-Einstein condensate (BEC) is theoretically investigated when it transversely passes through a red-detuned Gaussian field. Particular attentions are paid on the focusing (or defocusing) in shape and leading (or lagging) in position of the atoms, which are induced by a red-detuned (or blue-detuned) laser field. The time-dependent motion of BEC atoms and its final status are presented under the influences of the acceleration, the dipolar interaction between atom and optical field, as well as the s-wave scattering collisions of individual atoms. In addition, the acceleration only influences position of the atoms; an attractive or repulsive s-wave interaction can bring on a strong deformation to the atoms, making them collapse or diffusion in essence. Compared to the previous experiments, the findings are well consistent in the regime of a red-detuned laser field, moreover, an extension to the blue-detuned field is predicted. The results may provide more feasible ways for studying coherent atom-light manipulations in the field of ultra-cold atoms and molecules in the future.