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Motivated by the mechanism of inhibitory synapses, a new kind of spiking neural P (SNP) system rules, called inhibitory rules, is introduced in this paper. Based on this, a new variant of SNP systems is proposed, called spiking neural P systems with inhibitory rules (SNP-IR systems). Different from the usual firing rules in SNP systems, the firing condition of an inhibitory rule not only depends on the state of the neuron associated with the rule but also is related to the states of other neurons. Moreover, from the perspective of topological structure, the new variant is shown as a directed graph with inhibitory arcs, and therefore seems to have more powerful control. The computational completeness of SNP-IR systems is discussed. In particular, it is proved that SNP-IR systems are Turing universal number accepting/generating devices. Moreover, we obtain a small universal function-computing device for SNP-IR systems …