Deep learning based intelligent fault diagnosis methods have become a research hotspot in the fields of fault diagnosis and the health management of rolling bearings in recent years. To effectively identify incipient faults in rotating machinery, this paper proposes a novel hybrid intelligent fault diagnosis framework based on a convolutional neural network and support vector machine (SVM). First, an improved one-dimensional convolutional neural network (1DCNN) was adopted to extract fault features, and the state information and intrinsic properties of the raw vibration signals were mined. Second, the extracted features were used to train the SVM, which was applied to classify the fault category. The proposed hybrid framework combined the excellent classification performance of the SVM for small samples and the strong feature-learning ability of CNN network. In order to tune the parameters of the SVM, an improved novel particle swarm optimization algorithm (INPSO) which combined the Tent map and Lévy flight strategy was proposed. Numerical experimental results indicated that the proposed PSO variant had a better performance in searching accuracy and convergence speed. At last, multiple groups of rolling bearing fault diagnosis experiments were carried out and experimental results showed that, with the proposed 1DCNN-INPSO-SVM model, the hybrid framework was capable of diagnosing with high precision for rolling bearings and superior to some traditional fault diagnosis methods.