With noisy environment caused by fluoresence and additive white noise as well as complicated spectrum fingerprints, the identification of complex mixture materials remains a major challenge in Raman spectroscopy application. In this paper, we propose a new scheme based on a constant wavelet transform (CWT) and a deep network for classifying complex mixture. The scheme first transforms the noisy Raman spectrum to a two-dimensional scale map using CWT. A multi-label deep neural network model (MDNN) is then applied for classifying material. The proposed model accelerates the feature extraction and expands the feature graph using the global averaging pooling layer. The Sigmoid function is implemented in the last layer of the model. The MDNN model was trained, validated and tested with data collected from the samples prepared from substances in palm oil. During training and validating process, data augmentation is applied to overcome the imbalance of data and enrich the diversity of Raman spectra. From the test results, it is found that the MDNN model outperforms previously proposed deep neural network models in terms of Hamming loss, one error, coverage, ranking loss, average precision, F1 macro averaging and F1 micro averaging, respectively. The average detection time obtained from our model is 5.31 s, which is much faster than the detection time of the previously proposed models.