<p>Spiking neural P (SN P) systems were first proposed based on the function and structure of neurons and nervous systems, which are considered equivalent computational models to Turing machines. Neurons are important resources in SN P systems, which affect their computational power. In constructing universal SN P systems, the number of neurons is the topic of much research. This paper proposes an SN P variant, a spiking neural P system with one neuron (SNP-ON), that needs only one neuron to build a universal system. In SNP-ON systems, we adopt autapses, weights, and multiple channels to improve the computing power of the neuron and use different types of spikes to represent the numbers stored in eight registers. Instruction labels in register machines are distinguished by different numbers of spikes. Two universal SNP-ON systems are constructed in this work. The first, with 39 rules, is universal in computing functions; the second, with 38 rules, is capable of generating all Turing-computable numbers. Both systems use only one neuron.</p>