Due to the nature of Spiking Neural Networks (SNNs), it is challenging to be trained by biologically plausible learning principles. The multi-layered SNNs are with non-differential neurons, temporary-centric synapses, which make them nearly impossible to be directly tuned by back propagation. Here we propose an alternative biological inspired balanced tuning approach to train SNNs. The approach contains three main inspirations from the brain: Firstly, the biological network will usually be trained towards the state where the temporal update of variables are equilibrium (e.g. membrane potential); Secondly, specific proportions of excitatory and inhibitory neurons usually contribute to stable representations; Thirdly, the short-term plasticity (STP) is a general principle to keep the input and output of synapses balanced towards a better learning convergence. With these inspirations, we train SNNs with three steps: Firstly, the SNN model is trained with three brain-inspired principles; then weakly supervised learning is used to tune the membrane potential in the final layer for network classification; finally the learned information is consolidated from membrane potential into the weights of synapses by Spike-Timing Dependent Plasticity (STDP). The proposed approach is verified on the MNIST hand-written digit recognition dataset and the performance (the accuracy of 98.64%) indicates that the ideas of balancing state could indeed improve the learning ability of SNNs, which shows the power of proposed brain-inspired approach on the tuning of biological plausible SNNs.