Due to engineering limitations, the spatial-encoding gradient fields in MRI are not exactly linear across the entire field-of-view. If not properly accounted for during reconstruction, the gradient-nonlinearity (GNL) causes image distortion and artificial signal intensity change. Conventionally, the GNL effects are corrected after image reconstruction using image-domain interpolation, followed by intensity correction using the Jacobian-determinant of the distortion field. Images corrected using this method can suffer from noise amplification at regions with strong GNL distortion. Here, we develop a model-based reconstruction method with integrated GNL correction and constrained spatial support, and demonstrate reduced noise amplification effect using this method.