The noncentral Chi noise in magnitude image may significantly affect the reliability of quantitative analysis in diffusion-weighted (DW) magnetic resonance imaging (MRI), especially at high b-value and/or higher order modeling of diffusion signal such as diffusion kurtosis imaging (DKI). We developed a novel first-moment noise-corrected curve fitting model with adaptive neighborhood regularization (MN1CM-ANR) algorithm for DKI. By fitting the signal to its first-moment (i.e. the expectation of the signal), MN1CM-ANR can effectively compensate the bias due to the noncentral Chi noise. In addition, by exploiting the neighboring pixels to regularize the curve fitting, MN1CM-ANR can reduce the measurement variance.