The accuracy of conventional time delay estimation (TDE) algorithms is limited by the sampling interval. A novel algorithm of subsample TDE suitable for widehand signals is presented to improve the accuracy. This algorithm applies periodogram and parabolic interpolation to the cross correlation spectrum of band limited stochastic signals, and can obtain a continuous time delay estimator. Simulations are carried out to compare the performance of the proposed algorithm with that of other subsample TDE algorithms. Results show that the proposed algorithm outperforms other algorithms and reachs the Cramer-Rao lower bound (CRLB) at a high signal- to-noise ratio. For the wideband characteristic and the randomness of the transmitting signal, the proposed algo- rithm is suitable for the low probability of intercept radars.