Methods of generating a gradient waveform, gradient waveform generators and magnetic resonance imaging systems are provided. In one aspect, a first digital value is obtained by quantizing and coding spatial position information of a voxel of a subject according to the number of preset quantization bits, wherein the number of the quantization bits are more than the number of allowed input bits for a DAC; a second digital value is determined to be inputted into the DAC according to the first digital value and the number of the allowed input bits for the DAC; a quantization error is determined according to the first digital value and the second digital value; an error accumulating value is updated by accumulating the quantization error to the error accumulation value; the second digital value corrected according to the error accumulation value; and the corrected second digital value is inputted into the DAC.