Fast neutron computed tomography (FNCT) generally needs a longer measurement time because of low source strength and low detection efficiency. In order to reduce measurement time, methods of reducing single measurement time and the numbers of projection are employed, but, the two reductions lead to high statistics noise projections and sparse sampling. A good reconstruction algorithm can reduce the influence of these problems for reconstructed images. In this study, the maximum likelihood-expectation maximization algorithm (MLEM) based on the total variation algorithm (TV) and median root prior algorithm (MRP), named MLEM-TV-MRP has been proposed. The proposal incorporates the assumption of the Poisson distribution of projection noises, gradient image sparseness, and locally monotonous. The use of MLEM in the proposal was for reducing the influence of high statistics noise by considering the statistical characteristics of projection noise; the TV algorithm was employed to decrease the influence of sparse sampling by considering gradient image sparseness. Also, the MRP was introduced to remove artifacts and noise by considering the locally monotonous. In addition, a consistency-controlled steepest descent (CCSD) method and TV change method were respectively employed to adaptively adjust the iteration step-size of TV iteration and adaptively stop TV iteration in the proposed algorithm. A classical noise-free phantom was used to initially test the performance of the proposed algorithm- the results showed high-quality reconstruction. To further illustrate its performance in FNCT, a lead-polyethylene (Pb-CH2) sample with 25 high statistics noise projections was employed. SNR value of MLEM-TV-MRP showed an increase of about 62%, 40.7%, 36.7%, and 12.6% respectively as compared to the single-use of MLEM, MLEM-MRP, TV-POCS (projection on convex sets) and MLEM-TV. Also, the profile of the MLEM-TV-MRP algorithm is found to be closest to that of a reference image. In addition, the MLEM-TV-MRP has good convergence performance especlially in convergence value. The results have demonstrated that the proposed algorithm can greatly reduce the influences of few high statistical noise projections on reconstruction in FNCT.