In the health evaluation system of mechanical equipments， one of the most common situations is that the normal data is abundant and the fault data is scarce. Aiming at the defect that the convolutional neural network （CNN） has a low recognition accuracy of minority samples due to the imbalanced data， a countermeasure that incorporates a min-max objective （MMO） function into the convolutional neural network structure is adopted， and an intelligent fault identification method based on min-max objective CNN （MMOCNN） suitable for imbalanced data is proposed. Firstly， representative features learned from vibration signals by alternating convolution and pooling operations of the CNN are mapped to the class space through the fully connected layers（FC）. Then， the MMO function of the features is constructed in the class space. Finally， the MMO function is integrated into the loss function of the CNN. In the model training process， the overall classification error is considered to be the smallest， and the learned sample features are required to keep the smallest intra-class distance and the largest inter-class distance to achieve effective fault identification for imbalanced data. The imbalanced bearing datasets are used to test the identification of this method and the traditional CNN. Results show that the proposed method can improve the identification accuracy of minority samples by more than 20%. Other supporting experiments additionally confirm the effectiveness of the proposed method in the case of imbalanced data.