Parallel MRI (pMRI) is a way to increase the speed of the MRI acquisition by combining data obtained simultaneously from several receiver coils with distinct spatial sensitivities. The measured data contains additional information about the position of the signal with respect to data obtained by a standard, uniform sensitivity coil. The idea is to speed up the acquisition by sampling more sparsely in the k-space and to compensate the data loss using the additional information obtained by a higher number of receiver coils. Most parallel reconstruction methods work in image domain and estimate the reconstruction transformation independently in each pixel. We propose an algorithm that uses B-spline functions to approximate the reconstruction map which reduces the number of parameters to estimate and makes the reconstruction faster and less sensitive to noise. The proposed method is tested on both phantom and in vivo images. The results are compared with commercial implementation of GRAPPA and SENSE algorithms in terms of time complexity and quality of the reconstruction.