It is well known that the double integration of measured acceleration records is one of the most difficult signal processing, particularly in the measurements on civil engineering structures, The measured accelerations of civil engineering structures are usually non-stationary and contain non-gaussian low-frequency noises, which can be significant causes of numerical instabilities in double Integration, For the de-noising of this kind of signals, wavelet transform can be very effective because of its inherent processing features for non-stationary signals, In this paper, the de-noising algorithm for the double integration is proposed using the modified wavelet transform, which is extended version of ordinary wavelet transform to process non-gaussian and low-frequency noises, using the median filter concept, The example studies show that the integration can be improved by the proposed method.