A chemical shift MR method which utilizes a oscillating gradient field is presented in this paper. Frequency modulation resulting from oscillating a gradient field spreads the spectrum that contains both chemical shift and spatial information, over a wide frequency range by using a large modulation factor in FM. The chemical shift spectrum resides within every frequency band segmented by the modulation frequency ωm. The spectral elements gathered from all such frequency segments for a chemical shift frequency contain the spatial image of that particular chemical shift frequency, despite the distortion introduced by a series of the Bessel functions acting as a point spread function. A sum of several Bessel functions of the first kind Jn(. ) is used to approximate the deconvolution process, since the sum staggered with respect to n has a desirable peaking property useful in deconvolution. This leads to devise a new image reconstruction algorithm based on the simple moving average over the spatial coordinate for which the oscillating gradient is applied. Furthermore, the number of echo measurements necessary for an image size of N N is reduced from N2 of the spin echo chemical shift imaging down to N by this method. Simulation results supporting the validity of this method are also presented in this paper.