The composite binary offset carrier (CBOC) modulated signal contains multi-peaks in its auto-correlation function, which brings ambiguity to the signal acquisition process of a GNSS receiver. Currently, most traditional ambiguity-removing schemes for CBOC signal acquisition approximate CBOC signal as a BOC signal, which may incur performance degradation. Based on Galileo E1 CBOC signal, this paper proposes a novel adaptive ambiguity-removing acquisition scheme which doesn't adopt the approximation used in traditional schemes. According to the energy ratio of each sub-code of CBOC signal, the proposed scheme can self-adjust its local reference code to achieve unambiguous and precise signal synchronization. Monte Carlo simulation is conducted in this paper to analyze the performance of the proposed scheme and three traditional schemes. Simulation results show that the proposed scheme has higher detection probability and less mean acquisition time than the other three schemes, which verify the superiority of the proposed scheme.