It is very challenging to accurately unfold neutron spectrum based on multisphere neutron spectrometer because the unfolding problem is ill-posed. We transplant compressed-sensing (CS) theory, which has shown great potential for recovering signal based on under-sampled data, to neutron unfolding problem. Firstly, method of optimal directions (MOD) is employed for sparse representation of spectrums, and thus the unfolding problem is cast into CS formulation. Secondly, orthogonal matching pursuit (OMP) is applied to reconstruct coefficients of sparse representation, with which neutron spectrum can be recovered. Numerical simulation is conducted to validate effectiveness of the proposed method. The inherent difficulty of neutron unfolding is that one can only get uncomplete sample data of spectrums. Whereas, CS theory compensate the uncomplete data by exploiting sparse a priori information residing in spectrums, and thus benefit the unfolding quality. We conclude that it is meaningful to incorporate various a priori information in neutron unfolding algorithms.