This paper is concerned with the stability problem of uncertain linear neutral systems using a discretized Lyapunov functional approach. The uncertainty under consideration is linear fractional norm-bounded uncertainty which includes the routine norm-bounded uncertainty as a special case. A delay-dependent stability criterion is derived and is formulated in the form of linear matrix inequalities (LMIs). The criterion can be used to check the stability of linear neutral systems with both small and non-small delays. For nominal systems, the analytical results can be approached with fine discretization. For uncertainty systems with small delay, numerical examples show significant improvement over approaches in the literature. For uncertainty systems with non-small delay, the effect of the uncertainty on the maximum time-delay interval for asymptotic stability is also studied.