Power line communication (PLC) is one of the most attractive communication methods for in-home networks. However, the emissions of unwanted electric waves from PLC system cause harmful interference to other radio communication systems with the same frequency band. Wavelet OFDM (Orthogonal Frequency Division Multiplexing) is expected to be an efficient modulation for PLC because it can make steep and deep notch for any frequency band in the transmit signal power spectrum. However, wavelet OFDM cannot implement the equalization by guard interval (GI) like OFDM and causes performance degradation in multipath channels including power line channels. In this paper, we apply ASCET (Adaptive Sine modulated / Cosine modulated filter bank Equalizer for Transmultiplexers) to wavelet OFDM and evaluate its performance over a multipath power line channel. In particular, we propose an estimation scheme of equalizer coefficients for ASCET that the required preamble becomes short. We compare the performance of OFDM with GI to that of wavelet OFDM with ASCET over the multipath power line channel by computer simulations. As a result, we show that the proposed scheme can achieve the approximately equivalent performance of OFDM with GI by using the shorter preamble as compared to the original scheme.