Based on the matrix perturbation theory, the stability problem of the solution to accumulating GM(1,1) is studied. The research results show that the larger the order of accumulating is, the larger the perturbation bound is, and the perturbation bound is smaller when the newer data is perturbed under the equal perturbation. The traditional grey integer order accumulate method leads to the solution to model, which is contradictory with the principle of new information priority, thus the fractional order accumulating method is proposed. The contradiction is relieved and the perturbation bound is becoming smaller when the order is less than 1. A real example demonstrates the practicability and reliability of the proposed method.