ing at improving the quality of the neutron computed tomography (CT) reconstructed from high noise and sparse angle projection data, an iterative reconstruction method (SIRT-WTDM) combined the simultaneous iterative reconstruction technique (SIRT) and weighted total difference minimization (WTDM) is successfully proposed. The reconstructed images obtained by algebraic reconstruction technique, simultaneous algebraic reconstruction technique, and SIRT are compared with or without the random noise in the projections, from which the SIRT method is proved to have higher reconstruction accuracy and stronger anti-noise ability. Therefore, the SIRT method is adopted as the fidelity term of the neutron CT iterative reconstruction method with high-noise projections. Considering the constraint to the sparsity and the continuity of the image gradient, the WTDM method is adopted as the regularization term of the neutron CT iterative reconstruction method. Under the condition of extreme sparse angle projections, the SIRT-WTDM can obtain the better reconstruction images, which has been proved by the Shepp-Logan simulated data and cold neutron CT scanning data.