The output voltage of capacitor voltage transformer (CVT) is highly influential during initiation of contingencies due to its transient behaviour. This study proposes a novel method for fundamental component phasor estimation which reduces the transient impact of CVT. The proposed method (PM) first, based on hybrid full-cycle averaging window and also least squares (LS) technique, calculates the transient components of the CVT. In the next stage, by subtracting estimated transient behaviour from fault voltage signal, the fundamental phasor component of the obtained signal can be estimated utilising discrete Fourier transformer (DFT). Also, in order to prevent instability due to off-nominal frequency sampling rate, DFT formulation is improved. Several case studies have been carried out in order to show the robustness of the PM in the realistic simulation scenarios. Results show that the PM given in this study is able to estimate fundamental phasor voltage fault signal quickly and precisely with ignorable effect from transient impacts of CVT in almost always one cycle after fault occurrence.