The pulse-duration compression principle of a ultra-short laser pulse by cascaded second-order nonlinearity from a single β-barium borate (BBO) crystal was studied theoretically and experimentally. By using the split-step Fourier transformation and fourth-order Runge-Kutta methods, the type I coupled wave equations describing for Second Harmonic Generation (SHG) process of femtosecond pulse were simulated and calculated. The influences of the phase mismatch between fundamental harmonic(FH) and second harmonic(SH) pulses, the length of nonlinear crystal, peak intensity and the initial pulse-duration of the FH pulse on the pulse-duration compression were analyzed quantitatively and the experimental parameters were also optimized. Furthermore, the experiment of the pulse-width compression was performed for the ultra-short laser pulse with a center wavelength of 800 nm and a pulse width of 140 fs, and the pulse-width compression of more than two times was achieved. Finally, the experimental and simulation results for different fundamental peak intensities and initial pulse-widths were compared. Obtained results show that some factors like the phase mismatch between fundamental harmonic(FH) and second harmonic(SH) pulses, peak intensity, pulse chirp and the initial pulse-duration of the FH pulse have much influence on the pulse compression, so these facts mentioned above should be taken into consideration.