The training of Support Vector Machine (SVM) is an optimization problem of quadratic programming which can not be applied to the online training in real time applications or time-variant data source. The online algorithms proposed by other researchers have high computational complexity and slow training speed, which can not be well applied to the time-variant problems as well. In this paper the projection gradient and adaptive natural gradient is combined. The constraint projection adaptive natural gradient online algorithm for SVM is proposed. The computation complexity of the constraint projection adaptive natural gradient algorithm is . The learning performance is compared via prediction of the concentration of component A of Continuous Stirred Tank Reactor. The results of simulation demonstrate that the time taken by the constraint projection adaptive natural gradient online algorithm for SVM is far less than that of incremental algorithm, while keep higher prediction precision.