The submodular system k-partition problem is a problem of partitioning a given finite set V into k non-empty subsets V-1, V-2, ... , V-k so that Sigma(k)(i=1) f(V-i) is minimized where f is a non-negative submodular function on V, and k is a fixed integer. This problem contains the hypergraph k-cut problem. In this paper, we design the first exact algorithm for k = 3 and approximation algorithms for k >= 4. We also analyze the approximation factor for the hypergraph k-cut problem.