JFNK method is an efficient method for nonlinear problems. We consider two nonlinearities of neutron transport equation, the negative flux correction and the k-eigenvalue problem. The nonlinear problems are transformed into nonlinear residual equation form. And then we use JFNK method to solve them. We analyze impact of different constraints on the performance of JFNK, and compare JFNK method with NK method. LGMRES is used instead of restarting GMRES(m) method. Numerical results show that: ① Compared with SI method, JFNK has higher computational efficiency, even in the case of high scattering ratio; ② Difference approximation of Jacobian matrix-vector multiplication has no effect on the result, and the physics-based constraints are more efficient than standard mathematical constraints; ③ In addition, as an alternative to GMRES(m), LGMRES makes JFNK more efficient.