The fixing process for cycle ambiguity is a major issue for attitude determination using multiple Global Navigation Satellite System (GNSS) antennas. Existing algorithms have used pseudorange with large noise and ambiguity-included carrier phase measurements so the volume of the ambiguity search space is inevitably large. We propose a new algorithm to determine the attitude of a rotating vehicle using Doppler measurement in a closed form. Using differential and angular velocity estimation, we can reduce the size of the search space and the number of ambiguity candidates. We present simulation results using one master and two slave GNSS antennas. For all the cases in our simulations, the probability of one epoch fix is over 97%. Moreover, we achieved resolution of the ambiguity in two consecutive epochs. In other words, the maximum time-to-first-fixed-attitude (TTFFA) of our algorithm is only two seconds. Our algorithm can reduce the computation load in the ambiguity resolution for rotational vehicle attitude; consequently, it will be helpful in rapid and accurate determination in a case of phase lock loss due to a complex maneuver such as a fast spin.