In this paper, we propose a simple but effective way of improving the performance of channel estimation (CE) for pilot cyclic prefixed single carrier (PCP-SC) system. The proposed method utilizes the property that the shifting signal of the PCP pilot signal can also be utilized to estimate the channel information. The receiver can continuously estimate the channel information by just shifting the received pilot signal. Regardless of the signal-to-noise ratio (SNR) and the pilot type, the proposed method can achieve about a 1.72 dB performance gain in terms of the mean squared error (MSE) of channel estimation with a slight increase in computational complexity. The BER performance with the proposed CE improvement are evaluated in a multipath fading channel using a zero-forcing (ZF) equalizer and an minmum mean squared error (MMSE) equalizer by computer simulation. It is shown that the proposed CE improvment method using an MMSE equalizer which has an unbiased vlaue of noise variance (NV) estimator gives a promising BER performance. The proposed method also benefits the estimation of the SNR for the single carrier system.