Spiking neural p systems (SNP systems) are a distributed parallel computing device inspired by biology. A new variant—Weighted spiking neural P systems with target indications (WSNPTI systems) was proposed. By introducing the target indications into spiking neural P systems with weighted synapses, WSNPTI systems change the traditional spikes sending only to all synaptic connected neurons, but selectively sending the spikes to the specified neurons. WSNPTI systems simulate the workings of the human brain while using non-mechanical transmission methods to compute. This paper proves that the system is Turing universal as a number generation and an accepting device.