Orbit improvement with Doppler data is confronted with the systematic errors caused by the frequency offset of satellite beacon and station receiver. How to estimate the frequency offset of each topocentric passage is a key problem in evaluating the accuracy of orbit determination. The method of computing the frequency offset with the Guier navigation proposed in Ref.[1] has been proved in practice to be effective. However, calculations of the Guier navigation are rather complex, so it is difficult to use this algorithm in setting up the software for computing ephemerides by numerical integration. In this paper, a new algorithm based on the block inversions of the coefficient matrix of the normal equation is proposed. This algorithm merely requires the inversion of a 6 x 6 or 7 x 7 matrix, and then it is quite simple to calculate the frequency offset. As shown by simulations, the accuracy of orbit determination with the new algorithm is close to the Cramer-Rao lower bound, i.e., the theoretically optimal accuracy, and it is higher by about 15% than that of the Guier navigation algorithm.