Abstract: Different from traditional single-step algorithm,focus on satellite orbit integration from acceleration to position using new 12 steps Runge-kutta 2 orders algorithm.This algorithm is introduced in artificial satellite orbit application,and its integration results are studied and compared with other algorithms'.The results indicate that for integration precision and computation stability this algorithm is advanced,but it need more time consuming than others at same integration step.Synthetic consideration of the algorithm's stability whose integration error does not obviously increase with step length's augment,we can increase step length and decrease computation time to fulfill the needs of high-orbit satellite's orbit prediction and precise orbit determination.