Random vector functional ink (RVFL) networks belong to a class of single hidden layer neural networks in which some parameters are randomly selected. Their network structure in which contains the direct links between inputs and outputs is unique, and stability analysis and real-time performance are two difficulties of the control systems based on neural networks. In this paper, combining the advantages of RVFL and the ideas of online sequential extreme learning machine (OS-ELM) and initial-training-free online extreme learning machine (ITF-OELM), a novel online learning algorithm which is named as initial-training-free online random vector functional link algo rithm (ITF-ORVFL) is investigated for training RVFL. The link vector of RVFL network can be analytically determined based on sequentially arriving data by ITF-ORVFL with a high learning speed, and the stability for nonlinear systems based on this learning algorithm is analyzed. The experiment results indicate that the proposed ITF-ORVFL is effective in coping with nonparametric uncertainty.