Capacitive voltage transformers (CVTs) are widely used in line voltage measurement of EHV/UHV power systems. When a fault occurs, CVT measurements may contain severe transients during the beginning 3-6 fault cycles, which have usually been ignored instead of processed in many previous algorithms. However, this may cause reach problems and postpone response time in digital relay operation. In the present paper, dynamic phasor approach was employed to reconstruct line voltage phasors. Using the proposed algorithm, line voltage phasors can be obtained rapidly after one-cycle plus 2 samples, which are still accurate even if transients are involved in the CVT measurements. The proposed algorithm is simulated and evaluated by the MATLAB/SIMULINK built system. Simulation and evaluation results illustrate the effectiveness and performance of the proposed algorithm in various fault conditions and CVT types.