Apex-shifted multiples in CMP gathers are difficult to suppress and can seriously degrade seismic imaging results. To address this problem, we present a high-resolution Radon transform based on shifted hyperbolae with an additional apex-shift parameter. This transform allows focusing of apex-shifted events with a wide range of shapes, leading to a better separation and suppression of apex-shifted multiples. In order to make the transform computationally efficient, while obtaining good focusing in the multi-dimensional Radon domain, a restricted set of Radon parameter values is determined using a frequency-domain high-resolution Radon transform. A time-domain Radon transform is then performed on the restricted set of parameter values. The method is demonstrated on a synthetic data example involving apex-shifted pegleg multiples associated with a dipping seafloor. The multiples are successfully removed by muting in the Radon domain.