The discrimination function shaping method has been proposed to improve the anti‐multipath performance for a global navigation satellite system receiver. However, the existing methods fail to fully exploit the potential anti‐multipath performance of multiplexed binary offset carrier (MBOC)–modulated signals. In this paper, a code phase discrimination function shaping method is proposed for a Compass B1C quadrature MBOC‐modulated signal. The in‐phase binary offset carrier (BOC) (1,1) signal and quadrature‐phase BOC (6,1) signal replicas are designed according to the least squares estimation. Then a shifted cross‐correlation function (CCF) between the in‐phase BOC (1,1) signal and its pseudorandom noise code is multiplied with the obtained CCFs to ensure an unambiguous tracking. Finally, a discrimination function with a small pull‐in range can be obtained by a weighed combination of the in‐phase and quadrature‐phase CCFs. A computer simulation is conducted to assess the performances under multipath and thermal noise conditions.