This paper proposes a probabilistic spiking neural network (PSNN) with unimodal weight distribution, possessing long- and short-term plasticity. The proposed algorithm is derived by both the arithmetic gradient decent calculation and bioinspired algorithms. The algorithm is benchmarked by the Iris and Wisconsin breast cancer (WBC) data sets. The network features fast convergence speed and high accuracy. In the experiment, the PSNN took not more than 40 epochs for convergence. The average testing accuracy for Iris and WBC data is 96.7% and 97.2%, respectively. To test the usefulness of the PSNN to real world application, the PSNN was also tested with the odor data, which was collected by our self-developed electronic nose (e-nose). Compared with the algorithm (K-nearest neighbor) that has the highest classification accuracy in the e-nose for the same odor data, the classification accuracy of the PSNN is only 1.3% less but the memory requirement can be reduced at least 40%. All the experiments suggest that the PSNN is hardware friendly. First, it requires only nine-bits weight resolution for training and testing. Second, the PSNN can learn complex data sets with a little number of neurons that in turn reduce the cost of VLSI implementation. In addition, the algorithm is insensitive to synaptic noise and the parameter variation induced by the VLSI fabrication. Therefore, the algorithm can be implemented by either software or hardware, making it suitable for wider application.