The discrimination function shaping method has been proposed to improve the antimultipath 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. KEYWORDS global navigation satellite system, multipath effect, quadrature multiplexed binary offset carrier, shaping, tracking