In this paper, the regression learning algorithm with vector-valued RKHS is studied. We motivate the need for extending learning theory of scalar-valued functions and analze the learning performance. In this setting, the output data are from a Hilbert space YY, the associated RKHS consists of functions with values lie in YY. By providing mathematical aspects of vector-valued integral operator LKLK, the capacity independent error bounds and learning rates are derived by means of the integral operator technique.