The sampling algorithm of unscented Kalman filter(UKF), which selects the sigma points and their weights, plays a vital role for the accuracy and computational efficiency. It is well known that, more moments of random variables are matched, more accuracy reaches, for example, the Polynomial-extension of UKF(PUKF). However, such methods often suffer from their highly computational complexity, even worse, it is hard to get a solution. An efficient and highly accurate off-line algorithm is proposed for the Gaussian filter based on the high-order moments matching and linear-extension of UKF(LUKF). Experimental results show that the proposed algorithm has more accuracy than UKF and more computational efficiency than PUKF.