In this paper, a new algorithm based on Meshless Local Petrov-Galerking (MLPG) method is presented for analyzing the crack dynamic propagation. A new modified Moving Least Squares approximation is proposed to simplify the treatment of essential boundary conditions. Explicit central difference with lumped mass matrix is adopted for the time integral. Visibility criterion with crack edge node adding technique and the maximum hoop stress criterion are used to describe the crack propagation and forecast the crack propagation direction. Based on this algorithm, three-point bend specimen for impact fracture test is investigated. Comparing the results with those obtained by the laser caustic method and high-speed photographs, the accuracy of the present algorithm is proved.