The number of space targets in the LEO region is increasing， and the spacecraft orbital maneuvers are getting stronger and stronger. Combined with the demand for computational efficiency and accuracy of fast collision warning for LEO maneuvering targets， this paper proposes a short-term state error propagation method based on the state transfer tensor under the assumption of J2 model. The method introduces the second-order state transfer tensor to describe the nonlinear characteristics of error propagation from the perspective of spacecraft relative motion， gives the approximate analytical expression of error propagation， and completes the collision probability calculation on this basis. The simulation results show that the method proposed in the paper has good computational efficiency and accuracy for the short-term error propagation and collision probability calculation of LEO targets.