In view of the automatic recognition of Indonesian compound noun phrases, this paper proposes a method with Self-Attention mechanism, n-gram convolution kernel neural network and statistical model combined together so as to improve the performance of the existing multi-word expression extraction model. On the basis of the existing SHOMA model, a further improvement can be made by using the multi-layer CNN and Self-Attention mechanism, followed by an automatic recognition of compound noun phrases based on Indonesian data disclosed by Universal Dependencies. The comparative experiment results show that the F1 multi-word phrase recognition value of 32.20, as well as the F1 single-word recognition value of 32.34 obtained by TextCNN+Self-Attention+CRF model obtains respectively is 4.93% and 3.04% respectively higher than that of SHOMA model.