Spatial chirp is a common phenomena in ultrashort pulses. The focusing characteristics of Gaussian pulsed beams with the first-order spatial chirp (FSC) are investigated, and the analytical expression for the FSC beam on the output plane is derived. The analytical expressions for the pulse width, beam width and amplitude coupling coefficient of the FSC beam after focusing without chromatic aberration are derived. The intensity distribution before and after focusing is simulated. The pulse width, beam width and amplitude coupling coefficient of the FSC beam after focusing are analyzed numerically with the variation of propagation distance when the chromatic aberration is considered, which are compared with the corresponding results when the chromatic aberration is not considered. It is found that the FSC beam keeps the form after focusing without chromatic aberration; the chromatic aberration has no effect on beam width and amplitude coupling coefficient,but broadens the pulse width of FSC beam.