From the perspective of fractal geometry, the irregularity and complexity of near-fault ground motions and seismic responses of single degree of freedom (SDOF) are analyzed. Based on the box-counting method, the fractal dimensions of 30 acceleration time series of near-fault ground motions from Taiwan Chi-Chi earthquake and California Northridge earthquake are calculated. It is indicated that the acceleration time series of ground motions present the statistical fractal property, and the influence of characteristics of near-fault ground motions on their box dimensions is remarkable. Moreover, the box dimensions of ground motions reflect their frequency property to a large extent, and can be regarded as alternative index to represent their frequency content. Finally, for the time histories of seismic dynamic responses of elastic and inelastic SDOF systems subjected to near-fault ground motions, their box dimensions are computed to examine the fractal property.