Aiming at the problem of high-precision and fast bundle adjustment of multi-camera systems, a multi-camera fast bundle adjustment algorithm based on normalized matrix dimensionality reduction was proposed. Considering the fixed pose parameter relationship between the master and slave cameras in a multi-camera system, the system pose transformation matrix with the dimension of 3N (number of cameras)×4 was used. According to this matrix, each slave camera parameters could be quickly obtained from the master camera parameters, and the transformation relationship was taken into the bundle adjustment algorithm to get the posture of all slave cameras. For external parameters optimization of all cameras, only the external parameter of main camera need to be updated. So all cameras were bundled as a whole, which made the dimension of the Jacobian matrix and the normalized matrix relatively reduce. The calculation of multiple camera feature images could be implemented in one iteration, so the accuracy and speed of the algorithm have been greatly improved. According to simulation and practical measurement experiments, the optimization accuracy of the proposed algorithm is 15.5% higher than traditional bundle adjustment, and the operation efficiency is improved by 7.8%. These precise results can meet the practical engineering application requirements.