Accelerated parallel MRI has advantage in imaging speed, and its image quality has been improved continuously in recent years. This paper introduces a two-dimensional infinite impulse response model of inverse filter to replace the finite impulse response model currently used in generalized autocalibrating partially parallel acquisitions class image reconstruction methods. The infinite impulse response model better characterizes the correlation of k-space data points and better approximates the perfect inversion of parallel imaging process, resulting in a novel generalized image reconstruction method for accelerated parallel MRI. This k-space-based reconstruction method includes the conventional generalized autocalibrating partially parallel acquisitions class methods as special cases and has a new infinite impulse response data estimation mechanism for effective improvement of image quality. The experiments on in vivo MRI data show that the proposed method significantly reduces reconstruction errors compared with the conventional two-dimensional generalized autocalibrating partially parallel acquisitions method, particularly at the high acceleration rates.