This paper is concerned with finding a level ideal (LI) of a partially ordered set (poset): given a finite poset P, a level of each element p ∈ P is defined as the number of ideals which do not include p, then the problem is to find an ideal consisting of elements whose levels are less than a given integer i. We call the ideal as the i-th LI. The concept of the level ideal is naturally derived from the generalized median stable matching, that is a fair stable marriage introduced by Teo and Sethuraman (1998). Cheng (2008) showed that finding the i-th LI is #P-hard when i=Θ(N), where N is the total number of ideals of P. This paper shows that finding the i-th LI is #P-hard even if i=Θ(N1/c) where c≥1 is an arbitrary constant. Meanwhile, we give a polynomial time exact algorithm when i=O((logN)c′) where c′ is an arbitrary positive constant. We also devise two randomized approximation schemes using an oracle of almost uniform sampler for ideals of a poset.