Because of the improvement in radar resolution and decrease in grazing angle, the amplitude distribution of sea clutter obviously deviates from the Rayleigh distribution and presents a significant non-Gaussian feature. In this case, the compound Gaussian model is widely used. This study investigates the problem of detecting a target when signal mismatches occur in compound Gaussian clutter and proposes a selective detector to reject mismatched signals embedded in compound Gaussian clutter based on the so-called two-step Generalized Likelihood Ratio Test (GLRT). To design the selective detector, we modified the original hypothesis test by injecting a fictitious interference under the null hypothesis. These unwanted signals are assumed to be orthogonal to the nominal steering vector in the whitened subspace. The proposed detector has a Constant False Alarm Rate (CFAR) with respect to the statistics of the texture and covariance matrix. Finally, to demonstrate the effectiveness of the proposed detector, a Monte Carlo simulation is conducted to assess its performance based on the simulated and measured sea clutter data. The experimental results show that the proposed detector effectively improves the selectivity of the mismatched signals together with the detection of matched signals in a range spread target of 1～3 dB.