This paper proposes an improved acquisition method for high-order binary-offset-carrier (BOC) modulated signals based on fractal geometry. We introduced the principle of our acquisition method, and outlined its framework. We increase the main peak to side peaks ratio in the BOC autocorrelation function (ACF), with a simple fractal geometry transform. The proposed scheme is applicable to both generic high-order sine-and cosine-phased BOC-modulated signals. Simulation results show that the proposed method increases output signal to noise ratio (SNR).