Rydberg atom receiver attracts much research interest for promising applications in communications and sensing. Generally, Rydberg atomic receiver is utilized with microwave frequency comb (MFC) to expand its detectable frequency range. MFC consists of a set of equally spaced discrete frequency lines, resembling a comb in frequency space. In such receives, the mixing of RF signal and its closest MFC component excites the atoms into the desired Rydberg state. Since the mixing rather than RF signal is detected, there exists inevitable ambiguity of frequency estimation. In this paper, we provide a novel frequency ambiguity resolution based on improved Chinese remainder theorem (I-CRT). It realizes the instantaneous frequency estimation of RF signal with the MFC-based Rydberg atomic receiver. The effectiveness of proposed resolution in this paper is verified by both simulation experiments and theoretical analysis.