A full-energy dynamic model is developed to simulate the behavior and evolution of a free electron laser(FEL)pulse induced photoelectron wave-packet within an external single-cycle terahertz field, and the streaked photoelectron energy spectrum is significantly broadened at the zero crossing of terahertz vector potential, which could be used to retrieve the FEL pulse length. Further analysis and comparison of the pulse recovery errors of photoelectron wave packets with different pulse lengths at different delays, and the accuracy requirements of time synchronization in actual measurement are evaluated. In addition, a scheme for measuring the double -pulse delay is proposed, and the accuracy of the scheme is verified by numerical calculations.