It is widely accepted that appropriate network topology should be empirically predefined before training a specific neural network learning task. However, in most cases, these carefully designed networks are easily falling into two kinds of dilemmas: 1) When the data is not enough to train the network well, it will get an underfitting result. 2)When networks have learned too much patterns, they are likely to lead to an overfitting result and have a poor performance on processing new data or transferring to other tasks. Inspired by the synaptic pruning characteristics of the human brain, we propose a brain-inspired developmental neural network (BDNN) algorithm by adaptive synaptic pruning (BDNN-sp) which could get rid of the overfitting and underfitting. The BDNN-sp algorithm adaptively modulates network topology by pruning useless neurons dynamically. In addition, the evolutional optimization method makes the network stop on an appropriate network topology with the best consideration of accuracy and adaptability. Experimental results indicate that the proposed algorithm could automatically find the optimal network topology and the network complexity could adaptively increase along with the increase of task complexity. Compared to the traditional topology-predefined networks, trained BDNN-sp has the similar accuracy but better transfer learning abilities.