For the Multi-output Support Vector Regression (MSVR) algorithm based on gradient descent method in the process of model parameter fitting, the convergence rate is slow and the prediction accuracy is low. A modified version of the Quasi-Newton algorithm (BFGS) with second-order convergence rate based on the rank-2 correction rule was used to fit the model parameters of MSVR algorithm. At the same time, to ensure the decrease of the iterative process and the global convergence, the step size factor was determined by the non-exact linear search technique. Based on the analysis of the geometry structure of kernel function in Support Vector Machine (SVM), a data-dependent kernel function was substituted for the traditional kernel function, and the multi-output data-dependent kernel support vector regression model was generated. The model was compared with the multi-output support vector regression model based on gradient descent method and modified Newton method. The experimental results show that in the case of 200 samples, the iterative time of the proposed algorithm is 72.98 s, the iterative time of modified Newton's algorithm is 116.34 s and the iterative time of gradient descent method is 2065.22 s. The proposed algorithm can reduce the model iteration time and has faster convergence speed.