Instrument recognition plays very important roles in music information retrieval, sound source separation and automatic music transcription. However, due to different playing styles and audio qualities, this task cannot be accomplished easily. Simultaneous existence of multiple instruments in polyphonic music increases the challenge to a greater extent. This article mainly focus on the identification of the predominant instruments in polyphonic music. We propose to construct a network with an auxiliary classification designed based on the onset groups and instrument families. The principal classification and the auxiliary classification enable the network to learn the instrument categories and groups jointly in a pattern of multitask learning. The IRMAS datasetis adopted in the experiment to extract the mel-spectrogram and six other types of features. The micro and macro average of precisions, recalls and F1 measures are used to evaluate the classification results. The effect of multitask learning, batch normalization and center loss in the predominant instrument recognition are demonstrated by various experiments. By selecting the loss ratios through a development set, the micro and macro F1 measures of our proposed network can reach 0.685 and 0.597, which are 10.7% and 16.4% higher than those obtained by the baseline, the ConvNet presented in [1].