In this paper, the time fractals (D) for four moderately strong earthquake sequences are analysed using box counting algorithm. The four sequences have taken place in Lingwu-Wuzhong area of Ningxia since 1971 and have been recorded accurately. The results show that the time fractals are low (D<0.5) in this area. For the double main shock sequence or foreshock sequence, the fractal obtained before the second main shock occurrence is lower than that obtained from aftershock sequence. We have also analysed the frequency attenuation features of four earthquake sequences. It shows that the attenuation coefficient P and b value have synchronous variation. Therefore, we think that the earthquake sequence time fractal may be helpful for judging earthquake tendency in a short period.