Soliton-like pulse propagation, where the pulse intensity profile is conserved, except for its trailing edge, is found in a normal dispersive CS2-core optical fiber by a computer simulation. During propagation, it is found that the chirp of a pulse arising from the delayed nonlinear response compensates for the chirp arising from the second-order dispersion near the pulse peak position and the pulse experiences a negative frequency shift and a negative temporal shift. The effects of the instantaneous nonlinear response on the soliton-like pulse propagation are also evaluated, and the calculated spectrum agreed well with the experimental spectrum.