Recently, brain-inspired machine intelligence has gained great attention, research indicates that human brain grows in a self-organizing manner, especially in the visual cortex, fast object recognition is performed through distinct structures of neural connections and receptive fields. It is widely believed that such inhomogeneity is evolved through self-organizing by a process of neural plasticity. In this paper, a hierarchical self-organization spiking neural network (SOSNN) is proposed to solve the object recognition task with reinforcement plasticity rule, which simulates human visual cortex incorporating with many neural mechanisms like synaptic plasticity, homeostasis plasticity and lateral inhibitory. There are two phases in SOSNN which conform to the human visual pathway, feature extraction and decision-making (recognition). The object recognition task is performed in a manner of "end-to-end" in SOSNN since the network's decision is made by spiking activities in last layer without any external classifier. SOSNN is trained with reward-modulated spiking-time-dependent-plasticity (RM-STDP) rule in a reinforcement form, and the unsupervised STDP rule is also used to compare with RM-STDP. The classification experimental results on CIFAR and MNIST datasets show that SOSNN equipped with RM-STDP learning outperforms STDP and other existing unsupervised SNNs, which indicates the superiority of the proposed SOSNN in object recognition, and also testifies the reinforcement learning is an effective way to improve the performance of SNNs.