In order to decrease the length of the adaptive filter, this paper proposes a statistic model for adaptive algorithm in its early iterations as well as a novel algorithm for echo cancellation. The statistic model analyzes the expectation and variance of each coefficient of filter in the early iterations of adaptive algorithm. The modified algorithm based on this model identifies the location of the peak of the echo path and makes an estimation of the bulk delay. After the estimation a shorter adaptive filter centered about the peak coefficient is used to approach only the active coefficients instead of the whole echo path. Simulations with real echo path and theory both show that the peak coefficient is discriminated and the estimation of delay can be made in the early 75~100 iteration. A short filter is used to identify the echo path, which results in faster convergence speed and lower computational complexity.