The stability problem for the uncertain neutral system with distributed and discrete delays is researched. By delay-partitioning and constructing appropriate Lyapunov functional based on reciprocally convex combination and lower bound lemma, which is a way of handling a linear combination of positive functions weighted by the inverse of convex parameters(reciprocally convex combination), a robust stability criterion for the system is obtained in terms of the linear matrix inequalities(LMIs). The proposed approach allows the existence of time-variant delays, which can improve the robust performance of the neutral system. A numerical example is presented to illustrate the effectiveness and rationality of the results.