To study the role of bias in support vector regression (SVR), primal and dual optimization formulations of support vector regression optimization problem without bias (NBSVR) are proposed first, and the necessary condition of NBSVR optimization formulation’s global optima is presented and sub-optima solution of NBSVR dual problem has been proved for the dual problem of SVR then. An active set algorithm of dual optimization formulation without bias is proposed, and the linear convergence of the proposed algorithm has been proved. The experimental results on 21 benchmark datasets show that in the solution space of dual problem, SVR can only obtain the sub-optimal solution of NBSVR, the root mean square error (RMSE) of NBSVR tends to lower than SVR. The training time of NBSVR is not only less than SVR, but also less sensitive to kernel parameter.