Abstract: Under the condition of limited time window to access the measured values, a false data injection attack strategy in power grid based on random matrix is proposed. Multiple redundant sensor measurements were used to filter the influence of noise, and the best estimation of system state was obtained. An improved random matrix algorithm was introduced to construct false data injection attack vector to deal with the limited measurement that could not bypass the bad data detector with high probability. The important trade-off between the bypass probability of the bad data detector and its sparsity were described, so as to effectively ensure the spatial correlation of the attack. The IEEE bus system simulation verifies that the proposed method can enhance the probability of bypassing the bad data detector and enhance the attack effect.