Based on the theory of linear elastic fracture mechanics，a three-dimensional boundary element model of cylindrical gear with crack in tooth root is established and the stress intensity factor of crack tip is calculated. Then，through the automatic propagation analysis of initial crack，the growth trajectory and the propagation life of the crack at tooth root are obtained. Based on the obtained result，the influence of load magnitude，crack size，crack location and crack orientation on the crack propagation life is discussed. The results indicate that the tooth root crack expands slowly at first and then faster and faster；the crack propagates more easily along the tooth width than along the tooth thickness；the crack propagation life decreases with the increase of load magnitude or crack size，the effects of load magnitude on propagation life is significantly and the propagation life is more sensitive to initial crack depth than width；the propagation life is longer when crack is closer to the gear end-face and is shortest when crack has an initial direction about -30 degrees.