An effective and simple way to reconstruct displacement signal from a measured acceleration signal is proposed in this paper. To reconstruct displacement signal by means of double-integrating the time domain acceleration signal, the Nyquist frequency of the digital sampling of the acceleration signal should be much higher than the highest frequency component of the signal. On the other hand, to reconstruct displacement signal by taking the inverse Fourier transform, the magnitude of the significant frequency components of the Fourier transform of the acceleration signal should be greater than the 6 dB increment line along the frequency axis. With a predetermined resolution in time and frequency domain, determined by the sampling rate to measure and record the original signal, reconstructing high-frequency signals in the time domain and reconstructing low-frequency signals in the frequency domain will produce biased errors. Furthermore, because of the DC components inevitably included in the sampling process, low-frequency components of the signals are overestimated when displacement signals are reconstructed from the Fourier transform of the acceleration signal. The proposed method utilizes curve-fitting around the significant frequency components of the Fourier transform of the acceleration signal before it is inverse-Fourier transformed. Curve-fitting around the dominant frequency components provides much better results than simply ignoring the insignificant frequency components of the signal.