This paper presents a modified version of the existing cluster-based channel predictor (CBCP) which operates in the time domain on each individual multipath component and consists of a channel envelope predictor (EP) and a phase predictor (PP). Based on our investigation, the prediction accuracy of PP is lower than that of EP in the presence of estimation noise, which limits the performance of CBCP. The modified CBCP (M-CBCP) applies a smoothing on the increment of the estimated phases to improve the detection of the phase slope. The effect of the smoothing parameter selection in modified PP (M-PP) is studied. The increase in computational complexity due to the modification is almost negligible. Moreover, a physics-based scattering model is used to evaluate the performance of the proposed method.