In this paper we prove and discuss some new (H_p,L_p) type inequalities of maximal operators of Vilenkin-Nörlund means with non-decreasing coefficients. We also apply these inequalities to prove strong convergence theorems of such Vilenkin-N ¨orlund means. These inequalities are the best possible in a special sense. As applications, both some well-known and new results are pointed out.