The algorithm of Liu and Nguyen [IEEE Microw. Guided Wave Lett. 8 (1) (1998) 18; SIAM J. Sci. Comput. 21 (1) (1999) 283] for nonuniform fast Fourier transform (NUFFT) has been extended to two dimensions to reconstruct images using spiral MRI. The new gridding method, called LS_NUFFT, minimizes the reconstruction approximation error in the Least Square sense by generated convolution kernels that fit for the spiral k-space trajectories. For analytical comparison, the LS_NUFFT has been fitted into a consistent framework with the conventional gridding methods using Kaiser-Bessel gridding and a recently proposed generalized FFT (GFFT) approach. Experimental comparison was made by assessing the performance of the LS_NUFFT with that of the standard direct summation method and the Kaiser-Bessel gridding method, using both digital phantom data and in vivo experimental data. Because of the explicitly optimized convolution kernel in LS_NUFFT, reconstruction results showed that the LS_NUFFT yields smaller reconstruction approximation error than the Kaiser-Bessel gridding method, but with the same computation complexity.