A new non-coherent unambiguous tracking method for Cosine-phased Binary Offset Carrier (cosine-BOC) modulated signals based on an S-curve shaping technique is proposed in this letter. This method employs two linearly-combined codes to replace the commonly used multi-correlator structure. An asymmetrical S-curve without any false lock points is generated in the receiver, which is the product of the cross-correlation function between the received cosine-BOC signal and the local linearly-combined code and the cross-correlation function between the received cosine-BOC signal and another local linearly-combined code. Simulation results show that the proposed method has outstanding multipath mitigation performance while maintaining a sufficiently large operating range of the S-curve with both positive and negative delays.