The binary offset carrier(BOC) modulation is widely used in global navigation satellite system(GNSS) as a new signal modulation method. However, the inherent multi-peak feature of the autocorrelation function(ACF) of the BOC modulated signals makes the acquisition ambiguity problem likely to occur when using the traditional acquisition methods, resulting in the receiver finally giving wrong positioning results. In view of this, this paper proposes an unambiguous acquisition method based on the ACF time-shift combination of BOC modulated signals, and provides the corresponding acquisition circuit implementation structure. The proposed algorithm exploits the piecewise linearity of the ACF of BOC modulated signals and the feature that the autocorrelation value is 0 outside one chip width. The ACF of BOC modulated signals is time-shifted to the left and right respectively, and the two time-shifted results are multiplied by the ACF of BOC modulated signals to obtain a new synthetic correlation function. Meanwhile, in order to improve the main peak energy, the new function is divided into a normalized coefficient. Finally, the unambiguous correlation function that is applicable to all of modulation levels can be obtained. The simulation results show that the proposed algorithm can retain a single narrow main peak and eliminates all undesired secondary peaks under the condition of a certain degradation of detection performance, so as to achieve unambiguous acquisition of BOC modulated signals.