Improve performances of a convolutional neural network
It sounds like the model is underfit; to verify this, you would check that training and testing accuracy are similar, but, both lower than desired.

One cause is likely the very low number of training images for a model of this complexity. 

You could try augmenting the training set with transformations of those images, for example by rotating the images in the training set? (This was done in the original alexnet paper: http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf see section 4.1 on p.5).