Independent component analysis (ICA) has been a popular dimension reduction\ntool in statistical machine learning and signal processing. In this paper, we\npresent a convergence analysis for an online tensorial ICA algorithm, by\nviewing the problem as a nonconvex stochastic approximation problem. For\nestimating one component, we provide a dynamics-based analysis to prove that\nour online tensorial ICA algorithm with a specific choice of stepsize achieves\na sharp finite-sample error bound. In particular, under a mild assumption on\nthe data-generating distribution and a scaling condition such that $d^4/T$ is\nsufficiently small up to a polylogarithmic factor of data dimension $d$ and\nsample size $T$, a sharp finite-sample error bound of $\\tilde{O}(\\sqrt{d/T})$\ncan be obtained.\n