Recently, image recognization based on deep neural network has achieved good performance. However, research shows that neural networks are susceptible to adversarial attacks in the form of small perturbations to images, and a universal adversarial perturbation can even fool a network on the complete data set. Therefore, it is necessary to study the universal perturbation generation problem for constructing more robust neural networks. Universal perturbation generation aims to find a single pertubation that attacks the whole data set. Compared with image-specific pertubation generation, it requires more strict constraints and has higher computational complexity. Current methods produce universal perturbations with large norms perceptible to human vision. Based on optimization theory, this paper presents a new method which computes smaller universal perturbations under specified perturbation rate. The poposed algorithm first incorporates PCA (principal component analysis) to reduce problem dimension for good scalability; then by the superposition of mean image-specific pertubation and random noise, an initial universal perturbation satisfying the perturbation rate requirement can be obtained; finally, the norm of universal perburtation is reduced based on improved gradient descent method. Experiments demonstrate that the proposed approach can attack various state-of-the-art neural networks effectively: With the same pertubation rate, the norm of the pertubation given by the proposed method is 54\% smaller than the Uni. Perturbation algorithm on average.