Partially parallel imaging with localized sensitivities is a fast parallel image reconstruction method for both Cartesian and non-Cartesian trajectories, but suffers from aliasing artifacts when there are deviations from the assumption of perfect localization. Such reconstructions would normally crop the individual coil images to remove the artifacts prior to combination. However, the sampling densities in variable-density k-space trajectories support different field-of-views for separate regions in k -space. In fact, the higher sampling density of low frequencies can be used to reconstruct a bigger field-of-view without introducing aliasing artifacts and the resulting image signal-to-noise ratio (SNR) can be improved. A novel, fast variable-density parallel imaging method is presented, which reconstructs different field-of-views from separate frequencies according to the local sampling density in k-space. Aliasing-suppressed images can be produced with high SNR-efficiency without the need for accurate estimation of coil sensitivities and complex or iterative computations.